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 A145580 #6 Jun 02 2025 00:40:19 %S A145580 1,1,1,0,1,2,-1,0,2,3,0,-1,0,3,4,1,0,-2,0,4,6,0,1,0,-3,0,6,9,-1,0,2,0, %T A145580 -4,0,9,13,0,-1,0,3,0,-6,0,13,19,1,0,-2,0,4,0,-9,0,19,28 %N A145580 Eigentriangle, row sums = A000930. %C A145580 Row sums = A000930 starting with offset 1: (1, 1, 2, 3, 4, 6, 9, 13, 19,...). %C A145580 Sum of n-th row terms = rightmost term of next row. %F A145580 Let M = an infinite lower triangular matrix with (1, 1, 0, -1, 0, 1, 0, -1, 0, 1,...) in every column; and X = an infinite lower triangular matrix with A000930 as the main diagonal (offset 1): (1, 1, 2, 3, 4, 6, 9, 13, 19,...) and the rest zeros. Triangle A145580 = M * X. %e A145580 First few rows of the triangle = %e A145580 1; %e A145580 1, 1; %e A145580 0, 1, 2; %e A145580 -1, 0, 2, 3; %e A145580 0, -1, 0, 3, 4; %e A145580 1, 0, -2, 0, 4, 6; %e A145580 0, 1, 0, -3, 0, 6, 9; %e A145580 -1, 0, 2, 0, -4, 0, 9, 13; %e A145580 0, -1, 0, 3, 0, -6, 0, 13, 19; %e A145580 1, 0, -2, 0, 4, 0, -9, 0, 19, 28; %e A145580 ... %e A145580 Row 6 = (1, 0, -2, 0, 4, 6) = termwise products of (1, 0, -1, 0, 1, 1) and (1, 1, 2, 3, 4, 6). %Y A145580 A000930 %K A145580 tabl,sign %O A145580 1,6 %A A145580 _Gary W. Adamson_, Oct 13 2008