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 A117267 #16 Aug 10 2023 15:36:03 %S A117267 1,1,2,2,3,5,4,6,9,14,7,11,17,26,40,13,20,31,48,74,114,24,37,57,88, %T A117267 136,210,324,44,68,105,162,250,386,596,920,81,125,193,298,460,710, %U A117267 1096,1692,2612,149,230,355,548,846,1306,2016,3112,4804,7416 %N A117267 Difference row triangle of A117189. %C A117267 Take difference rows of A117189 (binomial transform of the tribonacci sequence, A000073); and reorient to a flush left format. %e A117267 Taking difference rows of A117189, we get: %e A117267 1, 2, 5, 14, 40, 114, ... %e A117267 1, 3, 9, 26, 74, ... %e A117267 2, 6, 17, 48, ... %e A117267 4, 11, 31, ... %e A117267 7, 20, ... %e A117267 13, ... %e A117267 Reorient into the triangle: %e A117267 1; %e A117267 1, 2; %e A117267 2, 3, 5; %e A117267 4, 6, 9, 14; %e A117267 7, 11, 17, 26, 40; %e A117267 ... %o A117267 (PARI) lista(nn) = my(va = Vec(-(x-1)^2/(-1+4*x-4*x^2+2*x^3) + O(x^(nn))), v = vector(nn)); v[1] = va; for (n=2, nn, v[n] = vector(nn-n+1, k, v[n-1][k+1] - v[n-1][k]);); my(list = List()); for (n=1, nn, my(i = n, j = 1); for (k=1, n, listput(list, v[i][j]); i--; j++;);); Vec(list); \\ _Michel Marcus_, Aug 10 2023 %Y A117267 Cf. A000073 (1st column), A117268 (difference rows), A117189 (right diagonal). %K A117267 nonn,tabl %O A117267 1,3 %A A117267 _Gary W. Adamson_, Mar 05 2006 %E A117267 More terms from _Michel Marcus_, Aug 10 2023