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Number of partitions of n into parts divisible by 4 or 5.
5

%I #12 Dec 01 2018 10:14:43

%S 1,0,0,0,1,1,0,0,2,1,2,0,3,2,2,3,5,3,4,3,11,5,6,6,15,13,10,9,23,17,23,

%T 15,34,27,31,33,50,40,48,45,86,60,71,69,116,106,105,102,169,144,176,

%U 150,237,211,240,248,335,299,347,338,506,425,487,487,681

%N Number of partitions of n into parts divisible by 4 or 5.

%C Also number of partitions of n with no part and no difference between two parts equal to 1,2,3,6,7 or 11.

%C Also number of partitions of n with no part appearing 1,2,3,6,7 or 11 times.

%H Seiichi Manyama, <a href="/A147786/b147786.txt">Table of n, a(n) for n = 0..10000</a>

%H A. E. Holroyd, <a href="http://arxiv.org/abs/0706.2282">Partition Identities and the Coin Exchange Problem</a>, arXiv:0706.2282 [math.CO], 2007.

%H A. E. Holroyd, <a href="https://doi.org/10.1016/j.jcta.2007.12.003">Partition Identities and the Coin Exchange Problem</a>, J. Combin. Theory Ser. A, 115 (2008) 1096-1101.

%F G.f.: Product_{k>=1} (1-x^(20k))/(1-x^(4k))/(1-x^(5k)).

%F a(n) ~ exp(2*Pi*sqrt(n/15))/(2*sqrt(30)*n). - _Vaclav Kotesovec_, Sep 23 2015

%t nmax = 60; CoefficientList[Series[Product[(1 + x^(5*k))*(1 + x^(10*k))/(1 - x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 23 2015 *)

%Y Cf. A007690, A147783, A147784, A147785, A147787.

%K nonn

%O 0,9

%A Alexander E. Holroyd (holroyd at math.ubc.ca)