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A147784
Number of partitions of n into parts divisible by 3 or 4.
5
1, 0, 0, 1, 1, 0, 2, 1, 2, 3, 2, 2, 7, 3, 4, 9, 9, 6, 15, 11, 15, 21, 19, 19, 39, 27, 32, 51, 51, 45, 78, 67, 82, 107, 104, 108, 172, 143, 165, 226, 232, 226, 328, 306, 356, 441, 446, 470, 655, 601, 677, 857, 891, 908, 1197, 1169, 1325, 1582
OFFSET
0,7
COMMENTS
Also number of partitions of n with no part and no difference between two parts equal to 1,2 or 5.
Also number of partitions of n with no part appearing 1,2 or 5 times.
LINKS
A. E. Holroyd, Partition Identities and the Coin Exchange Problem, arXiv:0706.2282 [math.CO], 2007.
A. E. Holroyd, Partition Identities and the Coin Exchange Problem, J. Combin. Theory Ser. A, 115 (2008) 1096-1101.
FORMULA
G.f.: Product_{k>=1} (1-x^(12k))/(1-x^(3k))/(1-x^(4k)).
a(n) ~ exp(sqrt(n/3)*Pi)/(4*sqrt(6)*n). - Vaclav Kotesovec, Sep 23 2015
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k))*(1 + x^(6*k))/(1 - x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander E. Holroyd (holroyd at math.ubc.ca)
STATUS
approved