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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 2 18:17 EDT 2020. Contains 334787 sequences. (Running on oeis4.)