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%I A036009 #8 May 10 2018 03:36:35
%S A036009 1,2,3,5,7,11,15,22,30,41,55,75,98,130,168,219,280,360,455,578,725,
%T A036009 910,1132,1410,1740,2149,2636,3232,3940,4801,5819,7050,8503,10245,
%U A036009 12298,14749,17625,21042,25045,29776,35305,41815,49400,58300,68648
%N A036009 Number of partitions of n into parts not of the form 25k, 25k+10 or 25k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 11 are greater than 1.
%C A036009 Case k=12,i=10 of Gordon Theorem.
%D A036009 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F A036009 a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * ((11*(3 + sqrt(5)))/30)^(1/4) / (10 * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t A036009 nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+10-25))*(1 - x^(25*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K A036009 nonn,easy
%O A036009 1,2
%A A036009 _Olivier Gérard_

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