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 A131402 #12 Sep 22 2024 02:02:19 %S A131402 1,1,1,1,3,1,1,4,4,1,1,6,7,6,1,1,7,14,14,7,1,1,9,20,33,20,9,1,1,10,31, %T A131402 56,56,31,10,1,1,12,40,97,111,97,40,12,1,1,13,55,142,217,217,142,55, %U A131402 13,1,1,15,67,213,358,463,358,213,67,15,1,1,16,86,287,590,841,841,590,287,86,16,1 %N A131402 2*A007318 - (A046854 + A065941 - A000012). %C A131402 Row sums = A131403: (1, 2, 5, 10, 21, 44, 93, ...). %H A131402 Andrew Howroyd, <a href="/A131402/b131402.txt">Table of n, a(n) for n = 0..1274</a> %F A131402 2*A007318 - (A046854 + A065941 - A000012) as infinite lower triangular matrices. %F A131402 T(n,k) = 2*binomial(n, k) + 1 - binomial(floor((n + k)/2), k) - binomial(n-floor((k+1)/2), floor(k/2)). - _Andrew Howroyd_, Aug 09 2018 %e A131402 First few rows of the triangle are: %e A131402 1; %e A131402 1, 1; %e A131402 1, 3, 1; %e A131402 1, 4, 4, 1; %e A131402 1, 6, 7, 6, 1; %e A131402 1, 7, 14, 14, 7, 1; %e A131402 1, 9, 20, 33, 20, 9, 1; %e A131402 1, 10, 31, 56, 56, 31, 10, 1; %e A131402 ... %o A131402 (PARI) T(n,k) = if(k <= n, 2*binomial(n, k) + 1 - binomial((n + k)\2, k) - binomial(n-(k+1)\2, k\2), 0) \\ _Andrew Howroyd_, Aug 09 2018 %Y A131402 Row sums are A131403. %Y A131402 Cf. A046854, A065941. %K A131402 nonn,tabl,easy %O A131402 0,5 %A A131402 _Gary W. Adamson_, Jul 07 2007 %E A131402 Missing terms inserted and a(55) and beyond from _Andrew Howroyd_, Aug 09 2018