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 A134513 #20 Jan 25 2025 23:01:24 %S A134513 1,1,1,1,1,1,2,2,1,1,1,3,3,1,1,3,3,4,4,1,1,1,6,6,5,5,1,1,4,4,10,10,6, %T A134513 6,1,1,1,10,10,15,15,7,7,1,1,5,5,20,20,21,21,8,8,1,1,1,15,15,35,35,28, %U A134513 28,9,9,1,1,6,6,35,35,56,56,36,36,10,10,1,1 %N A134513 Triangle read by rows: T(n, k) = binomial(ceiling((n+k)/2), floor((n-k)/2)). %C A134513 Old name: abs(A049310 * A097806). %C A134513 Equivalently, T(n,k) = A168561(n,k) + A168561(n,k+1). %C A134513 Row sums = A062114: (1, 2, 3, 6, 9, 16, 25, 42, 67, ...). %C A134513 Triangle A046854 = abs(A097806 * A049310). %F A134513 abs(A049310 * A097806) as infinite lower triangular matrices. %e A134513 First few rows of the triangle: %e A134513 1; %e A134513 1, 1; %e A134513 1, 1, 1; %e A134513 2, 2, 1, 1; %e A134513 1, 3, 3, 1, 1; %e A134513 3, 3, 4, 4, 1, 1; %e A134513 1, 6, 6, 5, 5, 1, 1; %e A134513 4, 4, 10, 10, 6, 6, 1, 1; %e A134513 1, 10, 10, 15, 15, 7, 7, 1, 1; %e A134513 ... %Y A134513 Cf. A046854, A049310, A062114, A097806. %K A134513 nonn,tabl %O A134513 0,7 %A A134513 _Gary W. Adamson_, Oct 28 2007 %E A134513 Better definition, offset changed to 0, and more terms from _Jinyuan Wang_, Jan 25 2025