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 A213945 Triangle by rows, generated from aerated sequences of 1's. 0

%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

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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)