On the number of generators for transeunt triangles (Q5929314)

A transeunt triangle of size \(n\) is an array of 0's and 1's in the shape of an equilateral triangle with side length \(n+1\). It is completely determined by the entries along any one side. Using them as the first row, subsequent rows are generated by taking the sums (modulo 2) of pairs of adjacent entries. Triangles are considered the same if they can be mapped to each other by rotation. The authors show that the number of different transeunt triangles of size \(n\) is asymptotic to \(2^{n+1}/3\). Two triangles can be added element-wise (modulo 2) to produce a third. The main question considered in this paper is the size of the smallest set which will generate all transeunt triangles of size \(n\) under this operation. The answer given (in Theorem 3.5) is unnecessarily complicated; it simplifies to \(\big\lceil(n+1)/3\big\rceil\).