A096653 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (3n)-dimensional partition numbers.

1, 0, 1, 0, 3, 1, 0, 6, 3, 1, 0, 13, 9, 3, 1, 0, 24, 19, 12, 3, 1, 0, 48, 48, 25, 15, 3, 1, 0, 86, 84, 84, 31, 18, 3, 1, 0, 160, 228, 99, 135, 37, 21, 3, 1, 0, 282, 129, 721, 57, 204, 43, 24, 3, 1, 0, 500, 2521, -2267, 2087, -93, 294, 49, 27, 3, 1, 0, 859, -16291, 29876, -13253, 5229, -417, 408, 55, 30, 3, 1, 0, 1479, 199621, -317919

Offset: 0

Author

Paul D. Hanna, Jul 06 2004

Keywords

• sign
• tabl

Comments

Row sums of T form A000293 (solid partitions); row sums of T^2 form A000416(6-D).

Examples

			Triangle T begins:
{1},
{0,1},
{0,3,1},
{0,6,3,1},
{0,13,9,3,1},
{0,24,19,12,3,1},
{0,48,48,25,15,3,1},
{0,86,84,84,31,18,3,1},
{0,160,228,99,135,37,21,3,1},
{0,282,129,721,57,204,43,24,3,1},
{0,500,2521,-2267,2087,-93,294,49,27,3,1},
{0,859,-16291,29876,-13253,5229,-417,408,55,30,3,1},
{0,1479,199621,-317919,165456,-46401,11539,-996,549,61,33,3,1},
{0,2485,-2547804,4150781,-2100853,627628,-126896,23006,-1926,720,67,36,3,1},...
Row sums are: {1,1,4,10,26,59,140,307,684,1464,3122,6500,...} (A000293).
T^2 begins:
{1},
{0,1},
{0,6,1},
{0,21,6,1},
{0,71,27,6,1},
{0,216,101,33,6,1},
{0,657,363,131,39,6,1},
{0,1907,1185,552,161,45,6,1},
{0,5507,3931,1824,789,191,51,6,1},
{0,15522,11574,7449,2520,1080,221,57,6,1},...
with row sums: {1,1,7,28,105,357,1197,3857,12300,38430,...} (A000416).
		

Crossrefs

Cf. A096651, A096652, A000293, A000416.

Formula

Matrix cube of triangle A096651.