This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179745 #16 Jul 16 2025 13:37:41 %S A179745 1,1,1,1,3,1,1,7,4,1,1,15,12,5,1,1,31,32,18,6,1,1,63,80,56,25,7,1,1, %T A179745 127,192,160,88,33,8,1,1,255,448,432,280,129,42,9,1 %N A179745 Triangle read by rows, derived from iterates of operations in which a current eigensequence becomes the left border of a new triangle; with triangles of the form: all 1's except the left border for triangles >1. %C A179745 Row sums of the triangle = odd-indexed Fibonacci numbers, A001519(n). %C A179745 Eigensequences of successive triangles tend to A001519: (1, 2, 5, 13, 34, ...). %F A179745 The triangle is derived from operations in two parts. First, form an array in which rows = eigensequences of triangles of the form: (all 1's except the left border). First triangle has all 1's. Eigensequence of this triangle = (1, 2, 4, 8, 16, 32, ...). We shift this to the right = (1, 1, 2, 4, 8, 16, ...); creating a new triangle with this sequence as the left border. Eigensequence of this triangle = (1, 2, 5, 12, 28, 64, ...). We shift this to the right, making it the left border of the next triangle; and so on such that eigensequence of current triangle becomes next triangle's left border. %F A179745 The second operation takes finite differences of the array. Reorienting the terms, we obtain the current triangle. %e A179745 First few rows of the array: %e A179745 1, 2, 4, 8, 16, 32, ... %e A179745 1, 2, 5, 12, 28, 64, ... %e A179745 1, 2, 5, 13, 33, 82, ... %e A179745 1, 2, 5, 13, 34, 88, ... %e A179745 1, 2, 5, 13, 34, 89, ... %e A179745 ... %e A179745 Taking finite differences from the top, we reorient the terms obtaining triangle: %e A179745 1; %e A179745 1, 1; %e A179745 1, 3, 1; %e A179745 1, 7, 4, 1; %e A179745 1, 15, 12, 5, 1; %e A179745 1, 31, 32, 18, 6, 1; %e A179745 1, 63, 80, 56, 25, 7, 1; %e A179745 1, 127, 192, 160, 88, 33, 8, 1; %e A179745 1, 255, 448, 432, 280, 129, 42, 9, 1; %e A179745 ... %Y A179745 Cf. A001519. %K A179745 nonn,tabl,more %O A179745 1,5 %A A179745 _Gary W. Adamson_, Jul 25 2010 %E A179745 Duplicate term removed by _Stefano Spezia_, Jul 16 2025