|
%I #3 Mar 30 2012 17:25:34
%S 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,
%T 113,56,48,36,25,14,0,15,248,113,112,72,60,35,22,0,22,503,248,226,168,
%U 120,84,55,30,0,30
%N Convolution triangle for A000293 (solid partitions): A000041 * A002836
%C Row sums = A000293, solid partitions: (1, 1, 4, 10, 26, 59, 140, 307, 684,...)
%F 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,... ...
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 2, 0, 2;
%e 5, 2, 0, 3;
%e 12, 5, 4, 0, 5;
%e 24, 12, 10, 6, 0, 7;
%e 56, 24, 24, 15, 10, 0, 11;
%e 113, 56, 48, 36, 25, 14, 0, 15;
%e 248, 113, 112, 72, 60, 35, 22, 0, 22;
%e 503, 248, 226, 168, 120, 84, 55, 30, 0, 30;
%e ...
%e Example: row 4 = (12, 5, 4, 0, 5), sum = 26 = A000293(4).
%Y Cf. A000293, A000041, A002836
%K nonn,tabl
%O 0,4
%A _Gary W. Adamson_, Jun 13 2009
|
