A177443 Triangle, row sums = A007729; derived from the generator for A002487, Stern's diatomic series.

1, 2, 0, 3, 1, 0, 3, 2, 0, 0, 3, 3, 2, 0, 0, 3, 3, 4, 0, 0, 0, 3, 3, 6, 1, 0, 0, 0, 3, 3, 6, 2, 0, 0, 0, 0, 3, 3, 6, 3, 3, 0, 0, 0, 0, 3, 3, 6, 3, 6, 0, 0, 0, 0, 0, 3, 3, 6, 3, 9, 2, 0, 0, 0, 0, 0, 3, 3, 6, 3, 9, 4, 0, 0, 0, 0, 0, 0, 3, 3, 6, 3, 9, 6, 3

Offset

0,2

Comments

Rows apparently tend to 3 * nonzero terms of Stern's diatomic series; i.e.,

3 * (1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5,...) = (3, 3, 6, 3, 9, 6, 9, 3, 12,...)

Row sums = A007729: (1, 2, 4, 5, 8, 10, 13, 14, ...)

Links

Table of n, a(n) for n=0..84.

Formula

Triangle read by rows, Q*R*S; where Q = an infinite lower triangular matrix with all 1's, R = the generator for A002487, and S = a diagonalized variant of A002487 (nonzero terms of A002487 as the right diagonal and the rest zeros). R, the generator for A002487 is an irregular lower triangular matrix with (1, 1, 1, 0, 0, 0,...) in each column; but each successive column for k>0 is shifted down twice from the previous column.

Example

First few rows of the triangle =
1;
2, 0;
3, 1, 0;
3, 2, 0, 0;
3, 3, 2, 0, 0;
3, 3, 4, 0, 0, 0;
3, 3, 6, 1, 0, 0, 0;
3, 3, 6, 2, 0, 0, 0, 0;
3, 3, 6, 3, 3, 0, 0, 0, 0;
3, 3, 6, 3, 6, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 2, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 4, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 3, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 6, 0, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 9, 1, 0, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 9, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 9, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0;
3, 3, 6, 3, 9, 6, 9, 3, 12, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0;
...

Crossrefs

Cf. A002487, A007729.

Sequence in context: A190440 A054372 A070679 * A176919 A220645 A127374

Adjacent sequences: A177440 A177441 A177442 * A177444 A177445 A177446

Keyword

nonn,tabl,uned

Author

Gary W. Adamson, May 08 2010

Status

approved