

A068980


Number of partitions of n into nonzero tetrahedral numbers.


20



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 / prod(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/(1x^(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. A226748, A003108.
Sequence in context: A071903 A091372 A185322 * A280950 A279135 A053266
Adjacent sequences: A068977 A068978 A068979 * A068981 A068982 A068983


KEYWORD

easy,nonn


AUTHOR

Franklin T. AdamsWatters, Apr 01 2002


STATUS

approved



