%I
%S 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 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 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 Triangle by rows, generated from aerated sequences of 1's.
%C 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 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 First few rows of the array are:
%e 1, 2, 4, 8, 16, 32, 64, 128, 256,...
%e 1, 1, 2, 3,..5,..8,.13,..21,..34,...
%e 1, 1, 1, 2,..3,..4,..6,...9,..13,...
%e 1, 1, 1, 1, 2,..3,..4,...5,...7,...
%e ... Then, take finite differences from the top > down, getting the triangle:
%e 1;
%e 1, 1;
%e 1, 1, 2;
%e 1, 1, 1, 5;
%e 1, 1, 1, 2, 11;
%e 1, 1, 1, 1, 4, 24;
%e 1, 1, 1, 1, 2, 7, 51;
%e 1, 1, 1, 1, 1, 4, 12, 107;
%e 1, 1, 1, 1, 1, 2, 6, 21, 222;
%e 1, 1, 1, 1, 1, 1, 4, 9, 36, 457;
%e ...
%Y Cf. A027934.
%K nonn,tabl
%O 0,6
%A _Gary W. Adamson_, Jun 25 2012
