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

Offset: 0

Author

Gary W. Adamson, Jun 25 2012

Keywords

• nonn
• tabl

Comments

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.

Examples

			First few rows of the array are:
1, 2, 4, 8, 16, 32, 64, 128, 256,...
1, 1, 2, 3,..5,..8,.13,..21,..34,...
1, 1, 1, 2,..3,..4,..6,...9,..13,...
1, 1, 1, 1,  2,..3,..4,...5,...7,...
... Then, take finite differences from the top -> down, getting the triangle:
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, 4, 12, 107;
1, 1, 1, 1, 1, 2, 6, 21, 222;
1, 1, 1, 1, 1, 1, 4, 9, 36, 457;
...
		

Crossrefs

Cf. A027934.

Formula

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.