A147787 - OEIS

%I #12 Dec 01 2018 10:15:32

%S 1,0,0,0,1,0,1,0,2,1,1,0,4,1,2,1,6,2,6,1,9,4,8,2,17,6,13,7,23,9,24,9,

%T 35,18,34,15,58,24,51,28,80,37,84,40,115,64,116,60,175,88,168,101,239,

%U 128,258,139,335,199,352,203,487,273,494,315,656,386,714

%N Number of partitions of n into parts divisible by 4,6 or 9.

%C Also number of partitions of n with no part and no difference between two parts equal to 1,2,3,5,7 or 11.

%C Also number of partitions of n with no part appearing 1,2,3,5,7 or 11 times.

%H Seiichi Manyama, <a href="/A147787/b147787.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^(12k))(1-x^(18k))/(1-x^(4k))/(1-x^(6k))/(1-x^(9k)).

%F a(n) ~ sqrt(7/6)*exp(sqrt(7*n/3)*Pi/3)/(12*n). - _Vaclav Kotesovec_, Sep 23 2015

%t nmax = 60; CoefficientList[Series[Product[(1 + x^(9*k))*(1 + x^(6*k))/(1 - x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 23 2015 *)

%Y Cf. A007690, A147783, A147784, A147785, A147786.

%K nonn

%O 0,9

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