Integer triangles basics
Author OpenLibMathSeq
1 Star
Updated Last
2 Years Ago
Started In
December 2019

Build status Docs dev

The package is tested against Julia >= 1.6.0 on Linux, macOS, and Windows64.

Very early in the development cycle.

Julia implementations of integer triangles.

We give a framework for computing mathematical integer triangles and use it to create so called "Integer Triangle Trait Cards".

A trait card is a compilation of the essential characteristics of an integer triangle, whereby we understand the characteristics of a triangle to be integer sequences that can be obtained from the triangle by elementary transformations.

To see what you can expect start by executing

using IntegerTriangles
TraitCard(BinomialTriangle, 8)

Overview tables can be automatically generated for a variety of triangles and traits.

A-Number Triangle Form Function Sequence
A000302 Binomial Std PolyVal3 1, 4, 16, 64, 256, 1024, 4096, 16384
A001333 SchroederB Inv AltSum 1, -1, 3, -7, 17, -41, 99, -239
A006012 SchroederL Inv AltSum 1, -2, 6, -20, 68, -232, 792, -2704
A026302 Motzkin Rev Central 1, 2, 9, 44, 230, 1242, 6853, 38376
A103194 Laguerre Std TransNat0 0, 1, 6, 39, 292, 2505, 24306, 263431
nothing Laguerre Rev TransNat1 1, 3, 15, 97, 753, 6771, 68983, 783945

Important: Note that we assume all sequences to start at offset = 0. Also note that all references to A-numbers are approximativ only, i.e. the first few terms of the sequence may differ and the OEIS-'offset' is always disregarded.

To use this feature you have to download the file stripped.gz from, expand it and put it in the directory ../data.

You can also look at the demo notebook.

An introduction to the project can be found in: