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 A131129 #10 Jan 27 2020 01:35:39 %S A131129 1,1,1,3,4,1,3,9,7,1,3,12,18,10,1,3,15,30,30,13,1,3,18,45,60,45,16,1, %T A131129 3,21,63,105,105,63,19,1,3,24,84,168,210,168,84,22,1 %N A131129 3*A007318 - 2*A097806, where A007318 = Pascal's triangle and A097806 = the pairwise operator. %C A131129 Row sums = A131128: (1, 2, 8, 20, 44, 92, 188, 380, ...), the binomial transform of (1, 1, 5, 1, 5, 1, 5, ...). Triangle A131108 has row sums (1, 2, 6, 14, 30, 62, ...), the binomial transform of (1, 1, 3, 1, 3, 1, ...). Generalization: Given triangles generated from N*A007318 - (N-1)*A097806, row sums are binomial transforms of (1, 1, (2N-1), 1, (2N-1), 1, ...). %C A131129 Triangle T(n,k), 0 <= k <= n, read by rows given by [1,2,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 18 2007 %F A131129 G.f.: (1-x*y+2*x^2+2*x^2*y)/((-1+x+x*y)*(x*y-1)). - _R. J. Mathar_, Aug 12 2015 %e A131129 First few rows of the triangle: %e A131129 1; %e A131129 1, 1; %e A131129 3, 4, 1; %e A131129 3, 9, 7, 1; %e A131129 3, 12, 18, 10, 1; %e A131129 3, 15, 30, 30, 13, 1; %e A131129 ... %Y A131129 Cf. A097806, A131128, A095121. %K A131129 nonn,tabl %O A131129 0,4 %A A131129 _Gary W. Adamson_, Jun 16 2007