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 A145579 #8 Jun 02 2025 00:40:13 %S A145579 1,1,1,0,1,2,1,0,2,3,1,1,0,3,6,0,1,2,0,6,11,1,0,2,3,0,11,20,1,1,0,3,6, %T A145579 0,20,37,0,1,2,0,6,11,0,37,68,1,0,2,3,0,11,20,0,68,125 %N A145579 Eigentriangle, row sums = A001590. %C A145579 Row sums = A001590 starting (1, 2, 3, 6, 11, 20, 37,...). %C A145579 Sum of n-th row terms = rightmost term of next row. %F A145579 Let M = an infinite lower triangular matrix with (1, 1, 0, 1, 1, 0,...) in every column and X = a diagonalized matrix of A001590: (1, 1, 2, 3, 6, 11, 20, 37,...), (i.e. A001590 starting with offset 3 as a diagonal prefaced with a 1; and the rest zeros). Triangle A145579 = M * X. %e A145579 First few rows of the triangle = %e A145579 1; %e A145579 1, 1; %e A145579 0, 1, 2; %e A145579 1, 0, 2, 3; %e A145579 1, 1, 0, 3, 6; %e A145579 0, 1, 2, 0, 6, 11; %e A145579 1, 0, 2, 3, 0, 11, 20; %e A145579 1, 1, 0, 3, 6, 0, 20, 37; %e A145579 0, 1, 2, 0, 6, 11, 0, 37, 68; %e A145579 1, 0, 2, 3, 0, 11, 20, 0, 68, 125; %e A145579 ... %e A145579 Row 7 = (1, 1, 0, 3, 6) = termwise products of (1, 1, 0, 1, 1) and (1, 1, 2, 3, 6). %Y A145579 A001590 %K A145579 nonn,tabl %O A145579 3,6 %A A145579 _Gary W. Adamson_, Oct 13 2008 %E A145579 Alignment of example rows and unintentional concatenation of values fixed by Charles J. Daniels (chajadan(AT)gmail.com), Dec 05 2009