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 A157424 #9 Jun 02 2025 01:24:56 %S A157424 1,0,1,0,0,1,1,0,0,1,0,1,0,0,2,1,0,1,0,0,3,0,1,0,1,0,0,5,1,0,1,0,1,0, %T A157424 0,7,1,1,0,1,0,3,0,0,11,1,1,1,0,2,0,5,0,0,0,17,0,1,1,1,0,3,0,7,0,0,27, %U A157424 1,0,1,1,2,0,5,0,11,0,0,40 %N A157424 Triangle read by rows, A157423 * (A052284 * 0^(n-k)). %C A157424 Row sums = A052284 starting at n=1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row. %F A157424 Triangle read by rows, A157423 * (A052284 * 0^(n-k)). A157423 = an infinite lower triangular matrix with A005171 in every column. (A052284 * 0^(n-k)) = an infinite lower triangular matrix with A052284: (1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...) as the main diagonal and the rest zeros. %e A157424 First few rows of the triangle = %e A157424 1; %e A157424 0, 1; %e A157424 0, 0, 1; %e A157424 1, 0, 0, 1; %e A157424 0, 1, 0, 0, 2; %e A157424 1, 0, 1, 0, 0, 3; %e A157424 0, 1, 0, 1, 0, 0, 5; %e A157424 1, 0, 1, 0, 2, 0, 0, 7; %e A157424 1, 1, 0, 1, 0, 3, 0, 0, 11; %e A157424 1, 1, 1, 0, 2, 0, 5,0, 0, 17; %e A157424 0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27; %e A157424 1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40; %e A157424 0, 1, 0, 1, 2, 3, 0, 7, 0, 17, 0, 0, 61; %e A157424 1, 0, 1, 0, 2, 3, 5, 0, 11, 0, 27, 0, 0, 92; %e A157424 ... %e A157424 Example: row 5 = (0, 1, 0, 0, 2) = termwise products of (0, 1, 0, 0, 1) and %e A157424 (1, 1, 1, 1, 2); where (0, 1, 0, 0, 2) = row 5 of triangle A157423 and %e A157424 (1, 1, 1, 1, 2) = the first 5 terms of A052284. %Y A157424 Cf. A157423, A005171, A052284 %K A157424 nonn,tabl %O A157424 1,15 %A A157424 _Gary W. Adamson_ & _Mats Granvik_, Feb 28 2009