A298269 Number of partitions of the n-th tetrahedral number into tetrahedral numbers.

1, 1, 2, 4, 11, 29, 94, 304, 1005, 3336, 11398, 38739, 132340, 451086, 1541074, 5242767, 17779666, 60048847, 202124143, 677000711, 2256910444, 7486274436, 24713275977, 81162110629, 265192045408, 862061443031, 2788194736946, 8972104829849, 28726271274133, 91515498561954, 290116750935925

Offset

0,3

Links

David A. Corneth, Table of n, a(n) for n = 0..500

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/(1 - x^A000292(k)).

a(n) = A068980(A000292(n)).

Example

a(3) = 4 because third tetrahedral number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

Table[SeriesCoefficient[Product[1/(1 - x^(k (k + 1) (k + 2)/6)), {k, 1, n}], {x, 0, n (n + 1) (n + 2)/6}], {n, 0, 30}]

Crossrefs

Cf. A000292, A037444, A068980, A072964, A298857.

Sequence in context: A339834 A148146 A148147 * A148148 A148149 A034769

Adjacent sequences: A298266 A298267 A298268 * A298270 A298271 A298272

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2018

Status

approved