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

0,6

Links

Table of n, a(n) for n=0..53.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

Formula

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

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

Example

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

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}]

Crossrefs

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

Sequence in context: A133091 A112204 A129710 * A070680 A351524 A054711

Adjacent sequences: A298854 A298855 A298856 * A298858 A298859 A298860

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2018

Status

approved