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A161564 Convolution triangle for A000293 (solid partitions): A000041 * A002836 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A209701 A158855 A005074 * A078182 A133394 A305628

Adjacent sequences:  A161561 A161562 A161563 * A161565 A161566 A161567

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 13 2009

STATUS

approved

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Last modified June 17 21:47 EDT 2019. Contains 324200 sequences. (Running on oeis4.)