A298857 Number of partitions of the n-th tetrahedral number into distinct tetrahedral numbers.

1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 5, 5, 10, 12, 17, 15, 22, 30, 56, 65, 72, 92, 172, 219, 299, 368, 478, 810, 1055, 1508, 1778, 2277, 3815, 5214, 7103, 8615, 11614, 18079, 24428, 33704, 42877, 56639, 85597, 116984, 159179, 199356, 268965, 400612, 545674, 740356, 950897, 1261597, 1842307

Offset: 0

Author

Ilya Gutkovskiy, Jan 27 2018

Keywords

• nonn

Examples

			a(5) = 2 because fifth tetrahedral number is 35 and we have [35] and [20, 10, 4, 1].
		

Links

• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index to sequences related to pyramidal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000292, A030273, A279278, A288126, A298269.

Programs

Mathematica

Table[SeriesCoefficient[Product[1 + x^(k (k + 1) (k + 2)/6), {k, 1, n}], {x, 0, n (n + 1) (n + 2)/6}], {n, 0, 53}]

Formula

a(n) = [x^A000292(n)] Product_{k>=1} (1 + x^A000292(k)).

a(n) = A279278(A000292(n)).