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

0,5

Comments

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

Links

Table of n, a(n) for n=0..81.

Formula

Matrix cube of triangle A096651.

Example

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.

Sequence in context: A096754 A021767 A071417 * A308639 A348191 A213668

Adjacent sequences: A096650 A096651 A096652 * A096654 A096655 A096656

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 06 2004

Status

approved