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 A213945 #11 Aug 07 2012 13:31:39 %S A213945 1,1,1,1,1,2,1,1,1,5,1,1,1,2,11,1,1,1,1,4,24,1,1,1,1,2,7,51,1,1,1,1,1, %T A213945 4,12,107,1,1,1,1,1,2,6,21,222,1,1,1,1,1,1,4,9,36,457,1,1,1,1,1,1,2,6, %U A213945 14,61,935,1,1,1,1,1,1,1,4,8,22,103,1904,1,1,1,1,1,1,1,2,6,11,34,173,3863 %N A213945 Triangle by rows, generated from aerated sequences of 1's. %C A213945 Row sums are powers of 2. The right border is a variant of A027934 in which the 0 of the latter is replaced by a 1. %F A213945 Form an array in which rows are INVERT transforms of sequences of 1's starting (1,1,1,...) with row 0; then the INVERT transforms of 1's aerated with one zero (row 1); with two zeros, (row 2); three zeros, (row 3); and so on. %e A213945 First few rows of the array are: %e A213945 1, 2, 4, 8, 16, 32, 64, 128, 256,... %e A213945 1, 1, 2, 3,..5,..8,.13,..21,..34,... %e A213945 1, 1, 1, 2,..3,..4,..6,...9,..13,... %e A213945 1, 1, 1, 1, 2,..3,..4,...5,...7,... %e A213945 ... Then, take finite differences from the top -> down, getting the triangle: %e A213945 1; %e A213945 1, 1; %e A213945 1, 1, 2; %e A213945 1, 1, 1, 5; %e A213945 1, 1, 1, 2, 11; %e A213945 1, 1, 1, 1, 4, 24; %e A213945 1, 1, 1, 1, 2, 7, 51; %e A213945 1, 1, 1, 1, 1, 4, 12, 107; %e A213945 1, 1, 1, 1, 1, 2, 6, 21, 222; %e A213945 1, 1, 1, 1, 1, 1, 4, 9, 36, 457; %e A213945 ... %Y A213945 Cf. A027934. %K A213945 nonn,tabl %O A213945 0,6 %A A213945 _Gary W. Adamson_, Jun 25 2012