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 A123682 #4 Mar 31 2012 13:23:38 %S A123682 1,0,1,1,1,1,0,2,2,1,1,1,3,3,1,0,2,2,4,4,1,1,1,3,3,5,5,1,0,2,2,4,4,6, %T A123682 6,1,1,1,3,3,5,5,7,7,1 %N A123682 First in an infinite series of triangular arrays which, when taken together, sum to 1,1,3,5,11,21,43,85,... cf. A001045. %C A123682 The starting row for each triangle is determined by the applicable source integer partition; thus for partitions 1,22,33,222,44,332,2222,333,... the starting rows are 1,4,6,6,8,8,8,9,... %e A123682 Summing the row sums of the triangular arrays we have %e A123682 1 1 %e A123682 1 1 %e A123682 3 3 %e A123682 5 5 0 %e A123682 11 9 2 %e A123682 21 13 7 1 0 %e A123682 43 19 18 4 2 %e A123682 85 25 36 12 10 2 %e A123682 ... %Y A123682 Cf. A059841 A001045 A123640. %K A123682 nonn,tabf %O A123682 1,8 %A A123682 _Alford Arnold_, Oct 06 2006