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 A214314 #13 May 14 2017 12:21:11 %S A214314 1,1,2,1,2,3,1,2,4,5,1,2,4,6,7,1,2,5,8,10,11,1,2,5,9,12,14,15,1,2,6, %T A214314 11,16,19,21,22,1,2,6,13,19,24,27,29,30,1,2,7,15,24,31,36,39,41,42,1, %U A214314 2,7,17,28,38,45,50,53,55,56,1,2,8,20,35,48,59,66,71,74,76,77 %N A214314 Number triangle with entry T(n,m) giving the position of the first partition of n with m parts in the Abramowitz-Stegun (A-St) partition ordering. %C A214314 For the Abramowitz-Stegun ordering of partitions see A036036 for the reference and a C. F. Hindenburg link. %C A214314 The present triangle is the partial sum triangle of the triangle t(n,k) = 0 if 0 <= n -1 < k , t(n,0) = 1, n >= 1 and t(n,k) = A008284(n,k) if n-1 >= k >= 1. This triangle with offset [1,0] for [n,k] is 1; 1,1; 1,1,1; 1,1,2,1; 1,1,2,2,1; 1,1,3,3,2,1;... (erase the diagonal of A008284 and add instead a column k=0 with only 1's). See the example section. %F A214314 T(n,m) = sum(p(n,k),k=0..m-1) if n >= m >= 1, otherwise 0, with p(n,0) :=1 and p(n,k) = A008284(n,k) for k=1,2,...,n-1. %e A214314 T(n,m) starts with: %e A214314 n\m 1 2 3 4 5 6 7 8 9 10 11 12... %e A214314 1 1 %e A214314 2 1 2 %e A214314 3 1 2 3 %e A214314 4 1 2 4 5 %e A214314 5 1 2 4 6 7 %e A214314 6 1 2 5 8 10 11 %e A214314 7 1 2 5 9 12 14 15 %e A214314 8 1 2 6 11 16 19 21 22 %e A214314 9 1 2 6 13 19 24 27 29 30 %e A214314 10 1 2 7 15 24 31 36 39 41 42 %e A214314 11 1 2 7 17 28 38 45 50 53 55 56 %e A214314 12 1 2 8 20 35 48 59 66 71 74 76 77 %e A214314 ... %e A214314 T(6,4) = 8 because the 11=T(6,6) partitions for n=6 are, in A-St order: [6]; [1,5],[2,4],[3,3]; [1^2,4],[1,2,3],[2^3]; [1^3,3],[1^2,2^2]; [1^4,2]; [1^6] and the first partition with 4 parts, appears at position 8. %e A214314 This triangle is obtained as partial sum triangle from the triangle t(n,k) (see the comment section) which starts with: %e A214314 n\m 0 1 2 3 4 5 6 7 8 9 10 11 ... %e A214314 1 1 %e A214314 2 1 1 %e A214314 3 1 1 1 %e A214314 4 1 1 2 1 %e A214314 5 1 1 2 2 1 %e A214314 6 1 1 3 3 2 1 %e A214314 7 1 1 3 4 3 2 1 %e A214314 8 1 1 4 5 5 3 2 1 %e A214314 9 1 1 4 7 6 5 3 2 1 %e A214314 10 1 1 5 8 9 7 5 3 2 1 %e A214314 11 1 1 5 10 11 10 7 5 3 2 1 %e A214314 12 1 1 6 12 15 13 11 7 5 3 2 1 %e A214314 ... %Y A214314 Cf. A008284. %K A214314 nonn,tabl %O A214314 1,3 %A A214314 _Wolfdieter Lang_, Jul 24 2012