login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A213945
Triangle by rows, generated from aerated sequences of 1's.
0
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.
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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 25 2012
STATUS
approved