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A068980
Number of partitions of n into nonzero tetrahedral numbers.
32
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
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).
Sequence in context: A091372 A185322 A324918 * A280950 A279135 A053266
KEYWORD
easy,nonn
AUTHOR
STATUS
approved