Package evaluation of IntegerTriangles on Julia 1.10.8 (92f03a4775*) started at 2025-02-25T11:05:31.922 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Set-up completed after 5.23s ################################################################################ # Installation # Installing IntegerTriangles... Resolving package versions... Installed LoadFlint ─ v0.5.1 Installed Nemo ────── v0.22.0 Updating `~/.julia/environments/v1.10/Project.toml` [715aea54] + IntegerTriangles v0.3.0 Updating `~/.julia/environments/v1.10/Manifest.toml` ⌅ [c3fe647b] + AbstractAlgebra v0.15.1 [1520ce14] + AbstractTrees v0.4.5 [b99e7846] + BinaryProvider v0.5.10 [a8cc5b0e] + Crayons v4.1.1 [9a962f9c] + DataAPI v1.16.0 [e2d170a0] + DataValueInterfaces v1.0.0 ⌅ [ffbed154] + DocStringExtensions v0.8.6 ⌅ [e30172f5] + Documenter v0.26.3 [35a29f4d] + DocumenterTools v0.1.20 [59287772] + Formatting v0.4.3 [d7ba0133] + Git v1.3.1 [708ec375] + Gumbo v0.8.3 ⌅ [cd3eb016] + HTTP v0.9.17 ⌅ [b5f81e59] + IOCapture v0.1.1 [83e8ac13] + IniFile v0.5.1 [715aea54] + IntegerTriangles v0.3.0 [82899510] + IteratorInterfaceExtensions v1.0.0 [692b3bcd] + JLLWrappers v1.7.0 [682c06a0] + JSON v0.21.4 ⌅ [472f376f] + LoadFlint v0.5.1 [739be429] + MbedTLS v1.1.9 ⌅ [2edaba10] + Nemo v0.22.0 [bac558e1] + OrderedCollections v1.8.0 [69de0a69] + Parsers v2.8.1 [aea7be01] + PrecompileTools v1.2.1 [21216c6a] + Preferences v1.4.3 ⌅ [08abe8d2] + PrettyTables v0.11.1 [fb686558] + RandomExtensions v0.4.4 [189a3867] + Reexport v1.2.2 [322a6be2] + Sass v0.2.0 [3783bdb8] + TableTraits v1.0.1 [bd369af6] + Tables v1.12.0 [5c2747f8] + URIs v1.5.1 ⌅ [e21ec000] + Antic_jll v0.200.400+0 ⌅ [d9960996] + Arb_jll v200.1900.1+0 [2e619515] + Expat_jll v2.6.5+0 ⌅ [e134572f] + FLINT_jll v200.700.100+0 [f8c6e375] + Git_jll v2.47.1+0 [528830af] + Gumbo_jll v0.10.2+0 [94ce4f54] + Libiconv_jll v1.18.0+0 [9bd350c2] + OpenSSH_jll v9.9.2+0 [458c3c95] + OpenSSL_jll v3.0.16+0 [47bcb7c8] + libsass_jll v3.6.6+0 [0dad84c5] + ArgTools v1.1.1 [56f22d72] + Artifacts [2a0f44e3] + Base64 [ade2ca70] + Dates [f43a241f] + Downloads v1.6.0 [7b1f6079] + FileWatching [b77e0a4c] + InteractiveUtils [b27032c2] + LibCURL v0.6.4 [76f85450] + LibGit2 [8f399da3] + Libdl [37e2e46d] + LinearAlgebra [56ddb016] + Logging [d6f4376e] + Markdown [a63ad114] + Mmap [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.10.0 [de0858da] + Printf [3fa0cd96] + REPL [9a3f8284] + Random [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization [6462fe0b] + Sockets [2f01184e] + SparseArrays v1.10.0 [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test [cf7118a7] + UUIDs [4ec0a83e] + Unicode [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [781609d7] + GMP_jll v6.2.1+6 [deac9b47] + LibCURL_jll v8.4.0+0 [e37daf67] + LibGit2_jll v1.6.4+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [3a97d323] + MPFR_jll v4.2.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.2+1 [14a3606d] + MozillaCACerts_jll v2023.1.10 [4536629a] + OpenBLAS_jll v0.3.23+4 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.2.1+1 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.52.0+1 [3f19e933] + p7zip_jll v17.4.0+2 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Building LoadFlint → `~/.julia/scratchspaces/44cfe95a-1eb2-52ea-b672-e2afdf69b78f/272bd4807361427f1e237ea15993c12ae945a6b1/build.log` Building Nemo ─────→ `~/.julia/scratchspaces/44cfe95a-1eb2-52ea-b672-e2afdf69b78f/ead8440767661649a3338f5a968a0946cc8262a4/build.log` Installation completed after 8.07s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompilation completed after 41.32s ################################################################################ # Testing # Testing IntegerTriangles Status `/tmp/jl_yao6ry/Project.toml` ⌅ [c3fe647b] AbstractAlgebra v0.15.1 ⌅ [ffbed154] DocStringExtensions v0.8.6 ⌅ [e30172f5] Documenter v0.26.3 [35a29f4d] DocumenterTools v0.1.20 ⌅ [cd3eb016] HTTP v0.9.17 [715aea54] IntegerTriangles v0.3.0 ⌅ [2edaba10] Nemo v0.22.0 [bac558e1] OrderedCollections v1.8.0 ⌅ [08abe8d2] PrettyTables v0.11.1 [b77e0a4c] InteractiveUtils [8dfed614] Test Status `/tmp/jl_yao6ry/Manifest.toml` ⌅ [c3fe647b] AbstractAlgebra v0.15.1 [1520ce14] AbstractTrees v0.4.5 [b99e7846] BinaryProvider v0.5.10 [a8cc5b0e] Crayons v4.1.1 [9a962f9c] DataAPI v1.16.0 [e2d170a0] DataValueInterfaces v1.0.0 ⌅ [ffbed154] DocStringExtensions v0.8.6 ⌅ [e30172f5] Documenter v0.26.3 [35a29f4d] DocumenterTools v0.1.20 [59287772] Formatting v0.4.3 [d7ba0133] Git v1.3.1 [708ec375] Gumbo v0.8.3 ⌅ [cd3eb016] HTTP v0.9.17 ⌅ [b5f81e59] IOCapture v0.1.1 [83e8ac13] IniFile v0.5.1 [715aea54] IntegerTriangles v0.3.0 [82899510] IteratorInterfaceExtensions v1.0.0 [692b3bcd] JLLWrappers v1.7.0 [682c06a0] JSON v0.21.4 ⌅ [472f376f] LoadFlint v0.5.1 [739be429] MbedTLS v1.1.9 ⌅ [2edaba10] Nemo v0.22.0 [bac558e1] OrderedCollections v1.8.0 [69de0a69] Parsers v2.8.1 [aea7be01] PrecompileTools v1.2.1 [21216c6a] Preferences v1.4.3 ⌅ [08abe8d2] PrettyTables v0.11.1 [fb686558] RandomExtensions v0.4.4 [189a3867] Reexport v1.2.2 [322a6be2] Sass v0.2.0 [3783bdb8] TableTraits v1.0.1 [bd369af6] Tables v1.12.0 [5c2747f8] URIs v1.5.1 ⌅ [e21ec000] Antic_jll v0.200.400+0 ⌅ [d9960996] Arb_jll v200.1900.1+0 [2e619515] Expat_jll v2.6.5+0 ⌅ [e134572f] FLINT_jll v200.700.100+0 [f8c6e375] Git_jll v2.47.1+0 [528830af] Gumbo_jll v0.10.2+0 [94ce4f54] Libiconv_jll v1.18.0+0 [9bd350c2] OpenSSH_jll v9.9.2+0 [458c3c95] OpenSSL_jll v3.0.16+0 [47bcb7c8] libsass_jll v3.6.6+0 [0dad84c5] ArgTools v1.1.1 [56f22d72] Artifacts [2a0f44e3] Base64 [ade2ca70] Dates [f43a241f] Downloads v1.6.0 [7b1f6079] FileWatching [b77e0a4c] InteractiveUtils [b27032c2] LibCURL v0.6.4 [76f85450] LibGit2 [8f399da3] Libdl [37e2e46d] LinearAlgebra [56ddb016] Logging [d6f4376e] Markdown [a63ad114] Mmap [ca575930] NetworkOptions v1.2.0 [44cfe95a] Pkg v1.10.0 [de0858da] Printf [3fa0cd96] REPL [9a3f8284] Random [ea8e919c] SHA v0.7.0 [9e88b42a] Serialization [6462fe0b] Sockets [2f01184e] SparseArrays v1.10.0 [fa267f1f] TOML v1.0.3 [a4e569a6] Tar v1.10.0 [8dfed614] Test [cf7118a7] UUIDs [4ec0a83e] Unicode [e66e0078] CompilerSupportLibraries_jll v1.1.1+0 [781609d7] GMP_jll v6.2.1+6 [deac9b47] LibCURL_jll v8.4.0+0 [e37daf67] LibGit2_jll v1.6.4+0 [29816b5a] LibSSH2_jll v1.11.0+1 [3a97d323] MPFR_jll v4.2.0+1 [c8ffd9c3] MbedTLS_jll v2.28.2+1 [14a3606d] MozillaCACerts_jll v2023.1.10 [4536629a] OpenBLAS_jll v0.3.23+4 [efcefdf7] PCRE2_jll v10.42.0+1 [bea87d4a] SuiteSparse_jll v7.2.1+1 [83775a58] Zlib_jll v1.2.13+1 [8e850b90] libblastrampoline_jll v5.11.0+0 [8e850ede] nghttp2_jll v1.52.0+1 [3f19e933] p7zip_jll v17.4.0+2 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. Testing Running tests... Test Summary: | Pass Total Time Laguerre | 13 13 2.7s A001333 SchroederB Inv AltSum [1 -1 3 -7 17 -41 99 -239 577 -1393 ] ┌──────────┬──────────┬──────┬───────────┬────────────────────────────────────────────────────────────┐ │ A-number │ Triangle │ Form │ Function │ Sequence │ ├──────────┼──────────┼──────┼───────────┼────────────────────────────────────────────────────────────┤ │ A000302 │ Binomial │ Std │ PolyVal3 │ 1, 4, 16, 64, 256, 1024, 4096, 16384 │ │ A111884 │ Lah │ Std │ TransAlts │ 1, -1, -1, -1, 1, 19, 151, 1091 │ │ A111884 │ Lah │ Std │ TransAlts │ 1, -1, -1, -1, 1, 19, 151, 1091 │ │ nothing │ Laguerre │ Rev │ TransNat1 │ 1, 3, 15, 97, 753, 6771, 68983, 783945, 9820737, 134352163 │ └──────────┴──────────┴──────┴───────────┴────────────────────────────────────────────────────────────┘ ================= Binomial Binomial Triangle [1 1 1 1 2 1 1 3 ] Binomial Reverse [1 1 1 1 2 1 1 3 ] Binomial Inverse [1 -1 1 1 -2 1 -1 3 ] Binomial RevInv [1 1 -1 1 -2 1 1 -3 ] Binomial InvRev [1 -1 1 1 -2 1 -1 3 ] Binomial DiagTri [1 1 1 1 1 2 1 3 ] Binomial ConvTri [1 1 2 1 4 6 1 6 ] Binomial PolyTri [1 1 1 1 2 1 1 4 ] Binomial Sum [1 2 4 8 16 32 64 128 ] Binomial EvenSum [1 1 2 4 8 16 32 64 ] Binomial OddSum [0 1 2 4 8 16 32 64 ] Binomial AltSum [1 0 0 0 0 0 0 0 ] Binomial DiagSum [1 1 2 3 5 8 13 21 ] Binomial Central [1 2 6 20 ] Binomial LeftSide [1 1 1 1 1 1 1 1 ] Binomial RightSide [1 1 1 1 1 1 1 1 ] Binomial PosHalf [1 3 9 27 81 243 729 2187 ] Binomial NegHalf [1 -1 1 -1 1 -1 1 -1 ] Binomial BinConv [1 2 6 20 70 252 924 3432 ] Binomial IBinConv [1 0 -2 0 6 0 -20 0 ] Binomial TransSqrs [0 1 6 24 80 240 672 1792 ] Binomial TransNat0 [0 1 4 12 32 80 192 448 ] Binomial TransNat1 [1 3 8 20 48 112 256 576 ] Binomial PolyVal2 [1 3 9 27 81 243 729 2187 ] Binomial PolyVal3 [1 4 16 64 256 1024 4096 16384 ] Triangle: [1] [1, 1] [1, 2, 1] [1, 3, 3, 1] [1, 4, 6, 4, 1] [1, 5, 10, 10, 5, 1] [1, 6, 15, 20, 15, 6, 1] [1, 7, 21, 35, 35, 21, 7, 1] Flat triangle: [1, 1, 1, 1, 2, 1, 1, 3] Inverse triangle: [1] [-1, 1] [1, -2, 1] [-1, 3, -3, 1] [1, -4, 6, -4, 1] [-1, 5, -10, 10, -5, 1] [1, -6, 15, -20, 15, -6, 1] [-1, 7, -21, 35, -35, 21, -7, 1] Inverse: [1, -1, 1, 1, -2, 1, -1, 3] Diagonal triangle: [1] [1] [1, 1] [1, 2] [1, 3, 1] [1, 4, 3] [1, 5, 6, 1] [1, 6, 10, 4] Diagonal: [1, 1, 1, 1, 1, 2, 1, 3] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [1, 4, 9, 16, 25, 36, 49, 64] [1, 8, 27, 64, 125, 216, 343, 512] [1, 16, 81, 256, 625, 1296, 2401, 4096] [1, 32, 243, 1024, 3125, 7776, 16807, 32768] [1, 64, 729, 4096, 15625, 46656, 117649, 262144] [1, 128, 2187, 16384, 78125, 279936, 823543, 2097152] Polynomial values, triangle: [1] [1, 1] [1, 2, 1] [1, 4, 3, 1] [1, 8, 9, 4, 1] [1, 16, 27, 16, 5, 1] [1, 32, 81, 64, 25, 6, 1] [1, 64, 243, 256, 125, 36, 7, 1] PolyVal: [1, 1, 1, 1, 2, 1, 1, 4] ================= Laguerre Laguerre Triangle [1 1 1 2 4 1 6 18 ] Laguerre Reverse [1 1 1 1 4 2 1 9 ] Laguerre Inverse [1 -1 1 2 -4 1 -6 18 ] Laguerre RevInv [1 1 -1 1 -4 2 1 -9 ] Laguerre DiagTri [1 1 2 1 6 4 24 18 ] Laguerre ConvTri [1 1 2 4 16 20 36 216 ] Laguerre PolyTri [1 1 1 2 2 1 6 7 ] Laguerre Sum [1 2 7 34 209 1546 13327 130922 ] Laguerre EvenSum [1 1 3 15 97 745 6571 65359 ] Laguerre OddSum [0 1 4 19 112 801 6756 65563 ] Laguerre AltSum [1 0 -1 -4 -15 -56 -185 -204 ] Laguerre DiagSum [1 1 3 10 43 225 1393 9976 ] Laguerre Central [1 4 72 2400 ] Laguerre LeftSide [1 1 2 6 24 120 720 5040 ] Laguerre RightSide [1 1 1 1 1 1 1 1 ] Laguerre PosHalf [1 3 17 139 1473 19091 291793 5129307 ] Laguerre NegHalf [1 -1 1 7 -127 1711 -23231 334391 ] Laguerre BinConv [1 2 11 88 905 11246 162607 2668436 ] Laguerre IBinConv [1 0 -5 22 9 -1244 14335 -79470 ] Laguerre TransSqrs [0 1 8 63 544 5225 55656 653023 ] Laguerre TransNat0 [0 1 6 39 292 2505 24306 263431 ] Laguerre TransNat1 [1 3 13 73 501 4051 37633 394353 ] Laguerre PolyVal2 [1 3 14 86 648 5752 58576 671568 ] Laguerre PolyVal3 [1 4 23 168 1473 14988 173007 2228544 ] Triangle: [1] [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 72, 16, 1] [120, 600, 600, 200, 25, 1] [720, 4320, 5400, 2400, 450, 36, 1] [5040, 35280, 52920, 29400, 7350, 882, 49, 1] Flat triangle: [1, 1, 1, 2, 4, 1, 6, 18] Inverse triangle: [1] [-1, 1] [2, -4, 1] [-6, 18, -9, 1] [24, -96, 72, -16, 1] [-120, 600, -600, 200, -25, 1] [720, -4320, 5400, -2400, 450, -36, 1] [-5040, 35280, -52920, 29400, -7350, 882, -49, 1] Inverse: [1, -1, 1, 2, -4, 1, -6, 18] Diagonal triangle: [1] [1] [2, 1] [6, 4] [24, 18, 1] [120, 96, 9] [720, 600, 72, 1] [5040, 4320, 600, 16] Diagonal: [1, 1, 2, 1, 6, 4, 24, 18] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [2, 7, 14, 23, 34, 47, 62, 79] [6, 34, 86, 168, 286, 446, 654, 916] [24, 209, 648, 1473, 2840, 4929, 7944, 12113] [120, 1546, 5752, 14988, 32344, 61870, 108696, 179152] [720, 13327, 58576, 173007, 414160, 866695, 1649232, 2921911] [5040, 130922, 671568, 2228544, 5876336, 13373190, 27422352, 51988748] Polynomial values, triangle: [1] [1, 1] [2, 2, 1] [6, 7, 3, 1] [24, 34, 14, 4, 1] [120, 209, 86, 23, 5, 1] [720, 1546, 648, 168, 34, 6, 1] [5040, 13327, 5752, 1473, 286, 47, 7, 1] PolyVal: [1, 1, 1, 2, 2, 1, 6, 7] ================= Lah Lah Triangle [1 0 1 0 2 1 0 6 ] Lah Reverse [1 1 0 1 2 0 1 6 ] Lah Inverse [1 0 1 0 -2 1 0 6 ] Lah RevInv [1 1 0 1 -2 0 1 -6 ] Lah DiagTri [1 0 0 1 0 2 0 6 ] Lah ConvTri [1 0 0 0 0 4 0 0 ] Lah PolyTri [1 0 1 0 1 1 0 3 ] Lah Sum [1 1 3 13 73 501 4051 37633 ] Lah EvenSum [1 0 1 6 37 260 2101 19362 ] Lah OddSum [0 1 2 7 36 241 1950 18271 ] Lah AltSum [1 -1 -1 -1 1 19 151 1091 ] Lah DiagSum [1 0 1 2 7 30 157 972 ] Lah Central [1 2 36 1200 ] Lah LeftSide [1 0 0 0 0 0 0 0 ] Lah RightSide [1 1 1 1 1 1 1 1 ] Lah PosHalf [1 1 5 37 361 4361 62701 1044205 ] Lah NegHalf [1 1 -3 13 -71 441 -2699 9157 ] Lah BinConv [1 1 5 37 361 4301 60001 954325 ] Lah IBinConv [1 1 -3 1 73 -699 3001 24697 ] Lah TransSqrs [0 1 6 39 292 2505 24306 263431 ] Lah TransNat0 [0 1 4 21 136 1045 9276 93289 ] Lah TransNat1 [1 2 7 34 209 1546 13327 130922 ] Lah PolyVal2 [1 2 8 44 304 2512 24064 261536 ] Lah PolyVal3 [1 3 15 99 801 7623 83079 1017495 ] Triangle: [1] [0, 1] [0, 2, 1] [0, 6, 6, 1] [0, 24, 36, 12, 1] [0, 120, 240, 120, 20, 1] [0, 720, 1800, 1200, 300, 30, 1] [0, 5040, 15120, 12600, 4200, 630, 42, 1] Flat triangle: [1, 0, 1, 0, 2, 1, 0, 6] Inverse triangle: [1] [0, 1] [0, -2, 1] [0, 6, -6, 1] [0, -24, 36, -12, 1] [0, 120, -240, 120, -20, 1] [0, -720, 1800, -1200, 300, -30, 1] [0, 5040, -15120, 12600, -4200, 630, -42, 1] Inverse: [1, 0, 1, 0, -2, 1, 0, 6] Diagonal triangle: [1] [0] [0, 1] [0, 2] [0, 6, 1] [0, 24, 6] [0, 120, 36, 1] [0, 720, 240, 12] Diagonal: [1, 0, 0, 1, 0, 2, 0, 6] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [0, 1, 2, 3, 4, 5, 6, 7] [0, 3, 8, 15, 24, 35, 48, 63] [0, 13, 44, 99, 184, 305, 468, 679] [0, 73, 304, 801, 1696, 3145, 5328, 8449] [0, 501, 2512, 7623, 18144, 37225, 68976, 118587] [0, 4051, 24064, 83079, 220096, 495475, 997056, 1846999] [0, 37633, 261536, 1017495, 2977216, 7306325, 15877728, 31535371] Polynomial values, triangle: [1] [0, 1] [0, 1, 1] [0, 3, 2, 1] [0, 13, 8, 3, 1] [0, 73, 44, 15, 4, 1] [0, 501, 304, 99, 24, 5, 1] [0, 4051, 2512, 801, 184, 35, 6, 1] PolyVal: [1, 0, 1, 0, 1, 1, 0, 3] ================= Catalan Catalan Triangle [1 0 1 1 0 1 0 2 ] Catalan Reverse [1 1 0 1 0 1 1 0 ] Catalan Inverse [1 0 1 -1 0 1 0 -2 ] Catalan RevInv [1 1 0 1 0 -1 1 0 ] Catalan DiagTri [1 0 1 1 0 0 2 2 ] Catalan ConvTri [1 0 0 1 0 2 0 0 ] Catalan PolyTri [1 0 1 1 1 1 0 2 ] Catalan Sum [1 1 2 3 6 10 20 35 ] Catalan EvenSum [1 0 2 0 6 0 20 0 ] Catalan OddSum [0 1 0 3 0 10 0 35 ] Catalan AltSum [1 -1 2 -3 6 -10 20 -35 ] Catalan DiagSum [1 0 2 0 5 0 14 0 ] Catalan Central [1 0 3 0 ] Catalan LeftSide [1 0 1 0 2 0 5 0 ] Catalan RightSide [1 1 1 1 1 1 1 1 ] Catalan PosHalf [1 1 5 9 45 97 485 1145 ] Catalan NegHalf [1 1 5 9 45 97 485 1145 ] Catalan BinConv [1 1 2 7 21 66 216 715 ] Catalan IBinConv [1 1 2 7 21 66 216 715 ] Catalan TransSqrs [0 1 4 11 28 66 152 339 ] Catalan TransNat0 [0 1 2 5 10 22 44 93 ] Catalan TransNat1 [1 2 4 8 16 32 64 128 ] Catalan PolyVal2 [1 2 5 12 30 74 185 460 ] Catalan PolyVal3 [1 3 10 33 110 366 1220 4065 ] Triangle: [1] [0, 1] [1, 0, 1] [0, 2, 0, 1] [2, 0, 3, 0, 1] [0, 5, 0, 4, 0, 1] [5, 0, 9, 0, 5, 0, 1] [0, 14, 0, 14, 0, 6, 0, 1] Flat triangle: [1, 0, 1, 1, 0, 1, 0, 2] Inverse triangle: [1] [0, 1] [-1, 0, 1] [0, -2, 0, 1] [1, 0, -3, 0, 1] [0, 3, 0, -4, 0, 1] [-1, 0, 6, 0, -5, 0, 1] [0, -4, 0, 10, 0, -6, 0, 1] Inverse: [1, 0, 1, -1, 0, 1, 0, -2] Diagonal triangle: [1] [0] [1, 1] [0, 0] [2, 2, 1] [0, 0, 0] [5, 5, 3, 1] [0, 0, 0, 0] Diagonal: [1, 0, 1, 1, 0, 0, 2, 2] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [0, 1, 2, 3, 4, 5, 6, 7] [1, 2, 5, 10, 17, 26, 37, 50] [0, 3, 12, 33, 72, 135, 228, 357] [2, 6, 30, 110, 306, 702, 1406, 2550] [0, 10, 74, 366, 1300, 3650, 8670, 18214] [5, 20, 185, 1220, 5525, 18980, 53465, 130100] [0, 35, 460, 4065, 23480, 98695, 329700, 929285] Polynomial values, triangle: [1] [0, 1] [1, 1, 1] [0, 2, 2, 1] [2, 3, 5, 3, 1] [0, 6, 12, 10, 4, 1] [5, 10, 30, 33, 17, 5, 1] [0, 20, 74, 110, 72, 26, 6, 1] PolyVal: [1, 0, 1, 1, 1, 1, 0, 2] ================= Motzkin Motzkin Triangle [1 1 1 2 2 1 4 5 ] Motzkin Reverse [1 1 1 1 2 2 1 3 ] Motzkin Inverse [1 -1 1 0 -2 1 1 1 ] Motzkin RevInv [1 1 -1 1 -2 0 1 -3 ] Motzkin DiagTri [1 1 2 1 4 2 9 5 ] Motzkin ConvTri [1 1 2 4 8 8 16 40 ] Motzkin PolyTri [1 1 1 2 2 1 4 5 ] Motzkin Sum [1 2 5 13 35 96 267 750 ] Motzkin EvenSum [1 1 3 7 19 51 141 393 ] Motzkin OddSum [0 1 2 6 16 45 126 357 ] Motzkin AltSum [1 0 1 1 3 6 15 36 ] Motzkin DiagSum [1 1 3 6 15 36 91 232 ] Motzkin Central [1 2 9 44 ] Motzkin LeftSide [1 1 2 4 9 21 51 127 ] Motzkin RightSide [1 1 1 1 1 1 1 1 ] Motzkin PosHalf [1 3 13 59 285 1419 7245 37659 ] Motzkin NegHalf [1 -1 5 -17 77 -345 1653 -8097 ] Motzkin BinConv [1 2 7 29 128 587 2759 13190 ] Motzkin IBinConv [1 0 -1 3 0 -5 15 0 ] Motzkin TransSqrs [0 1 6 26 100 361 1254 4245 ] Motzkin TransNat0 [0 1 4 14 46 147 462 1437 ] Motzkin TransNat1 [1 3 9 27 81 243 729 2187 ] Motzkin PolyVal2 [1 3 10 34 117 405 1407 4899 ] Motzkin PolyVal3 [1 4 17 73 315 1362 5895 25528 ] Triangle: [1] [1, 1] [2, 2, 1] [4, 5, 3, 1] [9, 12, 9, 4, 1] [21, 30, 25, 14, 5, 1] [51, 76, 69, 44, 20, 6, 1] [127, 196, 189, 133, 70, 27, 7, 1] Flat triangle: [1, 1, 1, 2, 2, 1, 4, 5] Inverse triangle: [1] [-1, 1] [0, -2, 1] [1, 1, -3, 1] [-1, 2, 3, -4, 1] [0, -4, 2, 6, -5, 1] [1, 2, -9, 0, 10, -6, 1] [-1, 3, 9, -15, -5, 15, -7, 1] Inverse: [1, -1, 1, 0, -2, 1, 1, 1] Diagonal triangle: [1] [1] [2, 1] [4, 2] [9, 5, 1] [21, 12, 3] [51, 30, 9, 1] [127, 76, 25, 4] Diagonal: [1, 1, 2, 1, 4, 2, 9, 5] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [2, 5, 10, 17, 26, 37, 50, 65] [4, 13, 34, 73, 136, 229, 358, 529] [9, 35, 117, 315, 713, 1419, 2565, 4307] [21, 96, 405, 1362, 3741, 8796, 18381, 35070] [51, 267, 1407, 5895, 19635, 54531, 131727, 285567] [127, 750, 4899, 25528, 103071, 338082, 944035, 2325324] Polynomial values, triangle: [1] [1, 1] [2, 2, 1] [4, 5, 3, 1] [9, 13, 10, 4, 1] [21, 35, 34, 17, 5, 1] [51, 96, 117, 73, 26, 6, 1] [127, 267, 405, 315, 136, 37, 7, 1] PolyVal: [1, 1, 1, 2, 2, 1, 4, 5] ================= Narayana Narayana Triangle [1 0 1 0 1 1 0 1 ] Narayana Reverse [1 1 0 1 1 0 1 3 ] Narayana Inverse [1 0 1 0 -1 1 0 2 ] Narayana RevInv [1 1 0 1 -1 0 1 -3 ] Narayana DiagTri [1 0 0 1 0 1 0 1 ] Narayana ConvTri [1 0 0 0 0 1 0 0 ] Narayana PolyTri [1 0 1 0 1 1 0 2 ] Narayana Sum [1 1 2 5 14 42 132 429 ] Narayana EvenSum [1 0 1 3 7 20 66 217 ] Narayana OddSum [0 1 1 2 7 22 66 212 ] Narayana AltSum [1 -1 0 1 0 -2 0 5 ] Narayana DiagSum [1 0 1 1 2 4 8 17 ] Narayana Central [1 1 6 50 490 ] Narayana LeftSide [1 0 0 0 0 0 0 0 ] Narayana RightSide [1 1 1 1 1 1 1 1 ] Narayana PosHalf [1 1 3 11 45 197 903 4279 ] Narayana NegHalf [1 1 -1 -1 5 -3 -21 51 ] Narayana BinConv [1 1 3 13 65 356 2072 12601 ] Narayana IBinConv [1 1 -1 -5 9 56 -120 -825 ] Narayana TransSqrs [0 1 5 22 95 406 1722 7260 ] Narayana TransNat0 [0 1 3 10 35 126 462 1716 ] Narayana TransNat1 [1 2 5 15 49 168 594 2145 ] Narayana PolyVal2 [1 2 6 22 90 394 1806 8558 ] Narayana PolyVal3 [1 3 12 57 300 1686 9912 60213 ] Triangle: [1] [0, 1] [0, 1, 1] [0, 1, 3, 1] [0, 1, 6, 6, 1] [0, 1, 10, 20, 10, 1] [0, 1, 15, 50, 50, 15, 1] [0, 1, 21, 105, 175, 105, 21, 1] Flat triangle: [1, 0, 1, 0, 1, 1, 0, 1] Inverse triangle: [1] [0, 1] [0, -1, 1] [0, 2, -3, 1] [0, -7, 12, -6, 1] [0, 39, -70, 40, -10, 1] [0, -321, 585, -350, 100, -15, 1] [0, 3681, -6741, 4095, -1225, 210, -21, 1] Inverse: [1, 0, 1, 0, -1, 1, 0, 2] Diagonal triangle: [1] [0] [0, 1] [0, 1] [0, 1, 1] [0, 1, 3] [0, 1, 6, 1] [0, 1, 10, 6] Diagonal: [1, 0, 0, 1, 0, 1, 0, 1] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1, 1] [0, 1, 2, 3, 4, 5, 6, 7, 8] [0, 2, 6, 12, 20, 30, 42, 56, 72] [0, 5, 22, 57, 116, 205, 330, 497, 712] [0, 14, 90, 300, 740, 1530, 2814, 4760, 7560] [0, 42, 394, 1686, 5028, 12130, 25422, 48174, 84616] [0, 132, 1806, 9912, 35700, 100380, 239442, 507696, 985032] [0, 429, 8558, 60213, 261780, 857405, 2326434, 5516133, 11814728] [0, 1430, 41586, 374988, 1967300, 7503330, 23151030, 61363736, 145043208] Polynomial values, triangle: [1] [0, 1] [0, 1, 1] [0, 2, 2, 1] [0, 5, 6, 3, 1] [0, 14, 22, 12, 4, 1] [0, 42, 90, 57, 20, 5, 1] [0, 132, 394, 300, 116, 30, 6, 1] PolyVal: [1, 0, 1, 0, 1, 1, 0, 2] ================= SchroederBig SchroederBig Triangle [1 2 1 6 4 1 22 16 ] SchroederBig Reverse [1 1 2 1 4 6 1 6 ] SchroederBig Inverse [1 -2 1 2 -4 1 -2 8 ] SchroederBig RevInv [1 1 -2 1 -4 2 1 -6 ] SchroederBig DiagTri [1 2 6 1 22 4 90 16 ] SchroederBig ConvTri [1 4 4 36 48 28 484 704 ] SchroederBig PolyTri [1 2 1 6 3 1 22 11 ] SchroederBig Sum [1 3 11 45 197 903 4279 20793 ] SchroederBig EvenSum [1 2 7 28 121 550 2591 12536 ] SchroederBig OddSum [0 1 4 17 76 353 1688 8257 ] SchroederBig AltSum [1 1 3 11 45 197 903 4279 ] SchroederBig DiagSum [1 2 7 26 107 468 2141 10124 ] SchroederBig Central [1 4 30 264 ] SchroederBig LeftSide [1 2 6 22 90 394 1806 8558 ] SchroederBig RightSide [1 1 1 1 1 1 1 1 ] SchroederBig PosHalf [1 5 33 253 2121 18853 174609 1667021 ] SchroederBig NegHalf [1 -3 17 -123 1001 -8739 79969 -756939 ] SchroederBig BinConv [1 3 15 89 575 3905 27391 196481 ] SchroederBig IBinConv [1 -1 -1 9 -33 97 -257 641 ] SchroederBig TransSqrs [0 1 8 49 276 1505 8100 43393 ] SchroederBig TransNat0 [0 1 6 31 156 785 3978 20335 ] SchroederBig TransNat1 [1 4 17 76 353 1688 8257 41128 ] SchroederBig PolyVal2 [1 4 18 86 426 2162 11166 58438 ] SchroederBig PolyVal3 [1 5 27 151 861 4969 28911 169187 ] Triangle: [1] [2, 1] [6, 4, 1] [22, 16, 6, 1] [90, 68, 30, 8, 1] [394, 304, 146, 48, 10, 1] [1806, 1412, 714, 264, 70, 12, 1] [8558, 6752, 3534, 1408, 430, 96, 14, 1] Flat triangle: [1, 2, 1, 6, 4, 1, 22, 16] Inverse triangle: [1] [-2, 1] [2, -4, 1] [-2, 8, -6, 1] [2, -12, 18, -8, 1] [-2, 16, -38, 32, -10, 1] [2, -20, 66, -88, 50, -12, 1] [-2, 24, -102, 192, -170, 72, -14, 1] Inverse: [1, -2, 1, 2, -4, 1, -2, 8] Diagonal triangle: [1] [2] [6, 1] [22, 4] [90, 16, 1] [394, 68, 6] [1806, 304, 30, 1] [8558, 1412, 146, 8] Diagonal: [1, 2, 6, 1, 22, 4, 90, 16] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [2, 3, 4, 5, 6, 7, 8, 9] [6, 11, 18, 27, 38, 51, 66, 83] [22, 45, 86, 151, 246, 377, 550, 771] [90, 197, 426, 861, 1610, 2805, 4602, 7181] [394, 903, 2162, 4969, 10602, 20939, 38578, 66957] [1806, 4279, 11166, 28911, 70078, 156591, 323694, 624631] [8558, 20793, 58438, 169187, 464334, 1172293, 2717318, 5828463] Polynomial values, triangle: [1] [2, 1] [6, 3, 1] [22, 11, 4, 1] [90, 45, 18, 5, 1] [394, 197, 86, 27, 6, 1] [1806, 903, 426, 151, 38, 7, 1] [8558, 4279, 2162, 861, 246, 51, 8, 1] PolyVal: [1, 2, 1, 6, 3, 1, 22, 11] ================= Jacobsthal Jacobsthal Triangle [1 1 1 1 2 1 3 5 ] Jacobsthal Reverse [1 1 1 1 2 1 1 3 ] Jacobsthal Inverse [1 -1 1 1 -2 1 -1 1 ] Jacobsthal RevInv [1 1 -1 1 -2 1 1 -3 ] Jacobsthal DiagTri [1 1 1 1 3 2 5 5 ] Jacobsthal ConvTri [1 1 2 1 4 6 9 30 ] Jacobsthal PolyTri [1 1 1 1 2 1 3 4 ] Jacobsthal Sum [1 2 4 12 32 88 240 656 ] Jacobsthal EvenSum [1 1 2 6 16 44 120 328 ] Jacobsthal OddSum [0 1 2 6 16 44 120 328 ] Jacobsthal AltSum [1 0 0 0 0 0 0 0 ] Jacobsthal DiagSum [1 1 2 5 11 26 59 137 ] Jacobsthal Central [1 2 10 52 ] Jacobsthal LeftSide [1 1 1 3 5 11 21 43 ] Jacobsthal RightSide [1 1 1 1 1 1 1 1 ] Jacobsthal PosHalf [1 3 9 51 225 1083 5049 23811 ] Jacobsthal NegHalf [1 -1 1 -9 17 -89 225 -937 ] Jacobsthal BinConv [1 2 6 28 130 612 2940 14296 ] Jacobsthal IBinConv [1 0 -2 4 2 -20 44 56 ] Jacobsthal TransSqrs [0 1 6 26 104 388 1384 4776 ] Jacobsthal TransNat0 [0 1 4 14 48 156 496 1544 ] Jacobsthal TransNat1 [1 3 8 26 80 244 736 2200 ] Jacobsthal PolyVal2 [1 3 9 33 117 417 1485 5289 ] Jacobsthal PolyVal3 [1 4 16 72 320 1424 6336 28192 ] Triangle: [1] [1, 1] [1, 2, 1] [3, 5, 3, 1] [5, 12, 10, 4, 1] [11, 27, 28, 16, 5, 1] [21, 62, 75, 52, 23, 6, 1] [43, 137, 193, 159, 85, 31, 7, 1] Flat triangle: [1, 1, 1, 1, 2, 1, 3, 5] Inverse triangle: [1] [-1, 1] [1, -2, 1] [-1, 1, -3, 1] [1, 4, 2, -4, 1] [-1, -7, 10, 4, -5, 1] [1, -14, -25, 16, 7, -6, 1] [-1, 65, -21, -55, 21, 11, -7, 1] Inverse: [1, -1, 1, 1, -2, 1, -1, 1] Diagonal triangle: [1] [1] [1, 1] [3, 2] [5, 5, 1] [11, 12, 3] [21, 27, 10, 1] [43, 62, 28, 4] Diagonal: [1, 1, 1, 1, 3, 2, 5, 5] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [1, 4, 9, 16, 25, 36, 49, 64] [3, 12, 33, 72, 135, 228, 357, 528] [5, 32, 117, 320, 725, 1440, 2597, 4352] [11, 88, 417, 1424, 3895, 9096, 18893, 35872] [21, 240, 1485, 6336, 20925, 57456, 137445, 295680] [43, 656, 5289, 28192, 112415, 362928, 999901, 2437184] Polynomial values, triangle: [1] [1, 1] [1, 2, 1] [3, 4, 3, 1] [5, 12, 9, 4, 1] [11, 32, 33, 16, 5, 1] [21, 88, 117, 72, 25, 6, 1] [43, 240, 417, 320, 135, 36, 7, 1] PolyVal: [1, 1, 1, 1, 2, 1, 3, 4] ================= Fibonacci Fibonacci Triangle [1 1 1 1 2 1 2 4 ] Fibonacci Reverse [1 1 1 1 2 1 1 3 ] Fibonacci Inverse [1 -1 1 1 -2 1 -1 2 ] Fibonacci RevInv [1 1 -1 1 -2 1 1 -3 ] Fibonacci DiagTri [1 1 1 1 2 2 3 4 ] Fibonacci ConvTri [1 1 2 1 4 6 4 16 ] Fibonacci PolyTri [1 1 1 1 2 1 2 4 ] Fibonacci Sum [1 2 4 10 24 58 140 338 ] Fibonacci EvenSum [1 1 2 5 12 29 70 169 ] Fibonacci OddSum [0 1 2 5 12 29 70 169 ] Fibonacci AltSum [1 0 0 0 0 0 0 0 ] Fibonacci DiagSum [1 1 2 4 8 16 32 64 ] Fibonacci Central [1 2 8 36 ] Fibonacci LeftSide [1 1 1 2 3 5 8 13 ] Fibonacci RightSide [1 1 1 1 1 1 1 1 ] Fibonacci PosHalf [1 3 9 39 153 615 2457 9831 ] Fibonacci NegHalf [1 -1 1 -5 9 -29 65 -181 ] Fibonacci BinConv [1 2 6 24 100 426 1848 8120 ] Fibonacci IBinConv [1 0 -2 2 4 -14 0 58 ] Fibonacci TransSqrs [0 1 6 25 92 313 1010 3137 ] Fibonacci TransNat0 [0 1 4 13 40 117 332 921 ] Fibonacci TransNat1 [1 3 8 23 64 175 472 1259 ] Fibonacci PolyVal2 [1 3 9 30 99 327 1080 3567 ] Fibonacci PolyVal3 [1 4 16 68 288 1220 5168 21892 ] Triangle: [1] [1, 1] [1, 2, 1] [2, 4, 3, 1] [3, 8, 8, 4, 1] [5, 15, 19, 13, 5, 1] [8, 28, 42, 36, 19, 6, 1] [13, 51, 89, 91, 60, 26, 7, 1] Flat triangle: [1, 1, 1, 1, 2, 1, 2, 4] Inverse triangle: [1] [-1, 1] [1, -2, 1] [-1, 2, -3, 1] [1, 0, 4, -4, 1] [-1, -3, 0, 7, -5, 1] [1, 2, -10, -2, 11, -6, 1] [-1, 9, 14, -19, -7, 16, -7, 1] Inverse: [1, -1, 1, 1, -2, 1, -1, 2] Diagonal triangle: [1] [1] [1, 1] [2, 2] [3, 4, 1] [5, 8, 3] [8, 15, 8, 1] [13, 28, 19, 4] Diagonal: [1, 1, 1, 1, 2, 2, 3, 4] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [1, 4, 9, 16, 25, 36, 49, 64] [2, 10, 30, 68, 130, 222, 350, 520] [3, 24, 99, 288, 675, 1368, 2499, 4224] [5, 58, 327, 1220, 3505, 8430, 17843, 34312] [8, 140, 1080, 5168, 18200, 51948, 127400, 278720] [13, 338, 3567, 21892, 94505, 320118, 909643, 2264072] Polynomial values, triangle: [1] [1, 1] [1, 2, 1] [2, 4, 3, 1] [3, 10, 9, 4, 1] [5, 24, 30, 16, 5, 1] [8, 58, 99, 68, 25, 6, 1] [13, 140, 327, 288, 130, 36, 7, 1] PolyVal: [1, 1, 1, 1, 2, 1, 2, 4] ================= Eulerian Eulerian Triangle [1 1 0 1 1 0 1 4 ] Eulerian Reverse [1 0 1 0 1 1 0 1 ] Eulerian InvRev [1 0 1 0 -1 1 0 3 ] Eulerian DiagTri [1 1 1 0 1 1 1 4 ] Eulerian ConvTri [1 1 0 1 2 1 1 8 ] Eulerian PolyTri [1 1 1 1 1 1 1 2 ] Eulerian Sum [1 1 2 6 24 120 720 5040 ] Eulerian EvenSum [1 1 1 2 12 68 360 2384 ] Eulerian OddSum [0 0 1 4 12 52 360 2656 ] Eulerian AltSum [1 1 0 -2 0 16 0 -272 ] Eulerian DiagSum [1 1 1 2 5 13 38 125 ] Eulerian Central [1 1 11 302 ] Eulerian LeftSide [1 1 1 1 1 1 1 1 ] Eulerian RightSide [1 0 0 0 0 0 0 0 ] Eulerian PosHalf [1 1 3 13 75 541 4683 47293 ] Eulerian NegHalf [1 1 -1 -3 15 21 -441 477 ] Eulerian BinConv [1 1 3 16 115 1056 11774 154624 ] Eulerian IBinConv [1 -1 -1 8 19 -276 -1002 21216 ] Eulerian TransSqrs [0 0 1 8 64 540 4920 48720 ] Eulerian TransNat0 [0 0 1 6 36 240 1800 15120 ] Eulerian TransNat1 [1 1 3 12 60 360 2520 20160 ] Eulerian PolyVal2 [1 1 3 13 75 541 4683 47293 ] Eulerian PolyVal3 [1 1 4 22 160 1456 15904 202672 ] Triangle: [1] [1, 0] [1, 1, 0] [1, 4, 1, 0] [1, 11, 11, 1, 0] [1, 26, 66, 26, 1, 0] [1, 57, 302, 302, 57, 1, 0] [1, 120, 1191, 2416, 1191, 120, 1, 0] Flat triangle: [1, 1, 0, 1, 1, 0, 1, 4] Inverse triangle: Diagonal triangle: [1] [1] [1, 0] [1, 1] [1, 4, 0] [1, 11, 1] [1, 26, 11, 0] [1, 57, 66, 1] Diagonal: [1, 1, 1, 0, 1, 1, 1, 4] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [1, 6, 13, 22, 33, 46, 61, 78] [1, 24, 75, 160, 285, 456, 679, 960] [1, 120, 541, 1456, 3081, 5656, 9445, 14736] [1, 720, 4683, 15904, 40005, 84336, 158095, 272448] [1, 5040, 47293, 202672, 606033, 1467376, 3088765, 5881968] Polynomial values, triangle: [1] [1, 1] [1, 1, 1] [1, 2, 1, 1] [1, 6, 3, 1, 1] [1, 24, 13, 4, 1, 1] [1, 120, 75, 22, 5, 1, 1] [1, 720, 541, 160, 33, 6, 1, 1] PolyVal: [1, 1, 1, 1, 1, 1, 1, 2] ================= Uni Uni Triangle [1 1 1 1 1 1 1 1 ] Uni Reverse [1 1 1 1 1 1 1 1 ] Uni Inverse [1 -1 1 0 -1 1 0 0 ] Uni RevInv [1 1 -1 1 -1 0 1 -1 ] Uni InvRev [1 -1 1 0 -1 1 0 0 ] Uni DiagTri [1 1 1 1 1 1 1 1 ] Uni ConvTri [1 1 2 1 2 3 1 2 ] Uni PolyTri [1 1 1 1 2 1 1 3 ] Uni Sum [1 2 3 4 5 6 7 8 ] Uni EvenSum [1 1 2 2 3 3 4 4 ] Uni OddSum [0 1 1 2 2 3 3 4 ] Uni AltSum [1 0 1 0 1 0 1 0 ] Uni DiagSum [1 1 2 2 3 3 4 4 ] Uni Central [1 1 1 1 ] Uni LeftSide [1 1 1 1 1 1 1 1 ] Uni RightSide [1 1 1 1 1 1 1 1 ] Uni PosHalf [1 3 7 15 31 63 127 255 ] Uni NegHalf [1 -1 3 -5 11 -21 43 -85 ] Uni BinConv [1 2 4 8 16 32 64 128 ] Uni IBinConv [1 0 0 0 0 0 0 0 ] Uni TransSqrs [0 1 5 14 30 55 91 140 ] Uni TransNat0 [0 1 3 6 10 15 21 28 ] Uni TransNat1 [1 3 6 10 15 21 28 36 ] Uni PolyVal2 [1 3 7 15 31 63 127 255 ] Uni PolyVal3 [1 4 13 40 121 364 1093 3280 ] Triangle: [1] [1, 1] [1, 1, 1] [1, 1, 1, 1] [1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1] Flat triangle: [1, 1, 1, 1, 1, 1, 1, 1] Inverse triangle: [1] [-1, 1] [0, -1, 1] [0, 0, -1, 1] [0, 0, 0, -1, 1] [0, 0, 0, 0, -1, 1] [0, 0, 0, 0, 0, -1, 1] [0, 0, 0, 0, 0, 0, -1, 1] Inverse: [1, -1, 1, 0, -1, 1, 0, 0] Diagonal triangle: [1] [1] [1, 1] [1, 1] [1, 1, 1] [1, 1, 1] [1, 1, 1, 1] [1, 1, 1, 1] Diagonal: [1, 1, 1, 1, 1, 1, 1, 1] Polynomial values, array: [1, 1, 1, 1, 1, 1, 1, 1] [1, 2, 3, 4, 5, 6, 7, 8] [1, 3, 7, 13, 21, 31, 43, 57] [1, 4, 15, 40, 85, 156, 259, 400] [1, 5, 31, 121, 341, 781, 1555, 2801] [1, 6, 63, 364, 1365, 3906, 9331, 19608] [1, 7, 127, 1093, 5461, 19531, 55987, 137257] [1, 8, 255, 3280, 21845, 97656, 335923, 960800] Polynomial values, triangle: [1] [1, 1] [1, 2, 1] [1, 3, 3, 1] [1, 4, 7, 4, 1] [1, 5, 15, 13, 5, 1] [1, 6, 31, 40, 21, 6, 1] [1, 7, 63, 121, 85, 31, 7, 1] PolyVal: [1, 1, 1, 1, 2, 1, 1, 3] The Laguerre triangle in different formats: Triangle in standard format: [1] [1, 1] [2, 4, 1] [6, 18, 9, 1] [24, 96, 72, 16, 1] [120, 600, 600, 200, 25, 1] [720, 4320, 5400, 2400, 450, 36, 1] Triangle as a nested array: Vector{Nemo.fmpz}[[1], [1, 1], [2, 4, 1], [6, 18, 9, 1], [24, 96, 72, 16, 1], [120, 600, 600, 200, 25, 1], [720, 4320, 5400, 2400, 450, 36, 1]] Triangle in flattened format: 1, 1, 1, 2, 4, 1, 6, 18, 9, 1, 24, 96, 72, 16, 1, 120, 600, 600, 200, 25, 1, 720, 4320, 5400, 2400, 450, 36, 1, Triangle in info format with sequence ID: [A021009] 1, 1, 1, 2, 4, 1, 6, 18, 9, 1, 24, 96, 72, 16, 1, ... Triangle in mapped format: 0 ↦ 1 1 ↦ 1 2 ↦ 1 3 ↦ 2 4 ↦ 4 5 ↦ 1 6 ↦ 6 7 ↦ 18 8 ↦ 9 9 ↦ 1 10 ↦ 24 11 ↦ 96 12 ↦ 72 13 ↦ 16 14 ↦ 1 15 ↦ 120 16 ↦ 600 17 ↦ 600 18 ↦ 200 19 ↦ 25 20 ↦ 1 21 ↦ 720 22 ↦ 4320 23 ↦ 5400 24 ↦ 2400 25 ↦ 450 26 ↦ 36 27 ↦ 1 Testing IntegerTriangles tests passed Testing completed after 26.67s PkgEval succeeded after 90.9s