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Number of partitions of n into parts not of the form 11k, 11k+2 or 11k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 4 are greater than 1.
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%I #8 Nov 21 2015 14:13:39

%S 1,1,2,3,4,6,8,11,14,19,24,32,40,51,65,82,101,127,156,193,236,289,350,

%T 427,514,620,744,893,1064,1271,1508,1790,2116,2500,2942,3464,4060,

%U 4758,5560,6494,7560,8801,10216,11852,13720,15870,18317,21133,24328

%N Number of partitions of n into parts not of the form 11k, 11k+2 or 11k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 4 are greater than 1.

%C Case k=5,i=2 of Gordon Theorem.

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

%F a(n) ~ sin(2*Pi/11) * 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; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 21 2015 *)

%K nonn,easy

%O 1,3

%A _Olivier Gérard_