A068980 Number of partitions of n into nonzero tetrahedral numbers.

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 11, 11, 12, 12, 15, 15, 16, 16, 19, 19, 22, 22, 25, 25, 28, 29, 32, 32, 35, 36, 42, 42, 45, 46, 52, 53, 56, 57, 63, 64, 70, 71, 77, 78, 84, 87, 94, 95, 101, 104, 115, 116, 122, 125, 136, 139, 146, 149, 160, 163, 175

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Zhicheng Gao, Andrew MacFie and Daniel Panario, Counting words by number of occurrences of some patterns, The Electronic Journal of Combinatorics, 18 (2011), #P143.

Formula

G.f.: 1 / Product_(k>=3} (1 - z^binomial(k, 3)).

G.f.: Sum_{i>=0} x^(i*(i+1)*(i+2)/6) / Product_{j=1..i} (1 - x^(j*(j+1)*(j+2)/6)). - Ilya Gutkovskiy, Jun 08 2017

Example

a(10) = 4 because we can write 10 = 10 = 4 + 4 + 1 + 1 = 4 + 1 + 1 + 1 + 1 + 1 = 1 + ... + 1.

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1-x^(k*(k+1)*(k+2)/6)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 09 2017 *)

Crossrefs

See also A007294 (partitions into triangular numbers), A000292 (tetrahedral numbers).

Cf. A003108, A226748.

Sequence in context: A091372 A185322 A324918 * A280950 A279135 A053266

Adjacent sequences: A068977 A068978 A068979 * A068981 A068982 A068983

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Apr 01 2002

Status

approved