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

0,6

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.

Links

Table of n, a(n) for n=0..90.

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.

Example

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.

Sequence in context: A127080 A216645 A216635 * A290771 A014651 A275422

Adjacent sequences: A213942 A213943 A213944 * A213946 A213947 A213948

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 25 2012

Status

approved