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 A131299 #25 Feb 24 2019 04:12:19 %S A131299 1,1,1,1,1,1,1,1,4,1,1,1,7,4,1,1,1,10,7,7,1,1,1,13,10,16,7,1,1,1,16, %T A131299 13,28,16,10,1,1,1,19,16,43,28,28,10,1,1,1,22,19,61,43,58,28,13,1,1,1, %U A131299 25,22,82,61,103,58,43,13,1,1,1,28,25,106,82,166 %N A131299 Triangle T(n,k) = 3*binomial(n-floor((k+1)/2), floor(k/2))-2 with k=0..n, read by rows. %C A131299 Row sums are in A131300. Reversed row triangle = A131301. %C A131299 From _R. J. Mathar_, Apr 08 2013: (Start) %C A131299 The matrix inverse starts %C A131299 1; %C A131299 -1, 1; %C A131299 0, -1, 1; %C A131299 0, 3, -4, 1; %C A131299 0, -6, 9, -4, 1; %C A131299 0, 30, -45, 21, -7, 1; %C A131299 0, -132, 198, -93, 33, -7, 1; %C A131299 0, 984, -1476, 693, -246, 54, -10, 1; %C A131299 0, -6756, 10134, -4758, 1689, -372, 72, -10, 1; %C A131299 0, 66972, -100458, 47166, -16743, 3687, -714, 102, -13, 1; %C A131299 (End) %H A131299 Nathaniel Johnston, <a href="/A131299/b131299.txt">Rows n = 0..100, flattened</a> %F A131299 3*A065941 - 2*A000012 as infinite lower triangular matrices. %e A131299 Triangle begins: %e A131299 1; %e A131299 1, 1; %e A131299 1, 1, 1; %e A131299 1, 1, 4, 1; %e A131299 1, 1, 7, 4, 1; %e A131299 1, 1, 10, 7, 7, 1; %e A131299 1, 1, 13, 10, 16, 7, 1; %e A131299 ... %p A131299 A131299 := proc(n,k) 3*binomial(n-floor((k+1)/2),floor(k/2))-2 ; end proc; # _Nathaniel Johnston_, Jun 30 2011 %Y A131299 Cf. A065941, A000012, A131300, A131301. %K A131299 nonn,tabl,easy %O A131299 0,9 %A A131299 _Gary W. Adamson_, Jun 27 2007 %E A131299 Better definition from _Bruno Berselli_, May 03 2012