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 A096653 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (3n)-dimensional partition numbers. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums of T form A000293 (solid partitions); row sums of T^2 form A000416(6-D). LINKS 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 * A213668 A256595 A004590 Adjacent sequences:  A096650 A096651 A096652 * A096654 A096655 A096656 KEYWORD sign,tabl AUTHOR Paul D. Hanna, Jul 06 2004 STATUS approved

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