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%I #14 May 11 2018 04:22:08
%S 1,1,2,3,5,6,9,12,17,22,30,38,51,64,83,104,133,164,207,254,316,386,
%T 475,576,704,848,1027,1232,1483,1768,2116,2512,2989,3534,4184,4926,
%U 5808,6812,7996,9348,10932,12735,14842,17238,20022,23188,26850,31008,35805
%N Number of partitions of n into parts not of the form 11k, 11k+5 or 11k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 4 are greater than 1.
%C Case k=5,i=5 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%H Seiichi Manyama, <a href="/A035948/b035948.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ cos(Pi/22) * sqrt(2) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Nov 21 2015
%t nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 21 2015 *)
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
%E a(0)=1 prepended by _Seiichi Manyama_, May 08 2018
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