A161564 Convolution triangle for A000293 (solid partitions): A000041 * A002836

1, 0, 1, 2, 0, 2, 5, 2, 0, 3, 12, 5, 4, 0, 5, 24, 12, 10, 6, 0, 7, 56, 24, 24, 15, 10, 0, 11, 113, 56, 48, 36, 25, 14, 0, 15, 248, 113, 112, 72, 60, 35, 22, 0, 22, 503, 248, 226, 168, 120, 84, 55, 30, 0, 30

Offset

0,4

Comments

Row sums = A000293, solid partitions: (1, 1, 4, 10, 26, 59, 140, 307, 684,...)

Links

Table of n, a(n) for n=0..54.

Formula

Triangle read by rows, A000041 convolved with A002836: (1, 0, 2, 5, 12, 24, 56,...). Antidiagonals of a convolution array, A002836 * A000041: 1, . 1, . 2, . 3, . 5, . 7, . 11,... 0, . 0, . 0, . 0, . 0, . 0, .. 0,... 2, . 2, . 4, . 6, .10, .14, ..22,... 5, . 5, . 10, .15, .25, .35, ..55,... 12 .12, . 24, .36, .60, .84, .132,... ...

Example

First few rows of the triangle =
1;
0, 1;
2, 0, 2;
5, 2, 0, 3;
12, 5, 4, 0, 5;
24, 12, 10, 6, 0, 7;
56, 24, 24, 15, 10, 0, 11;
113, 56, 48, 36, 25, 14, 0, 15;
248, 113, 112, 72, 60, 35, 22, 0, 22;
503, 248, 226, 168, 120, 84, 55, 30, 0, 30;
...
Example: row 4 = (12, 5, 4, 0, 5), sum = 26 = A000293(4).

Crossrefs

Cf. A000293, A000041, A002836

Sequence in context: A158855 A344908 A005074 * A078182 A363803 A133394

Adjacent sequences: A161561 A161562 A161563 * A161565 A161566 A161567

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 13 2009

Status

approved