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%I A213423 #15 Jun 02 2018 06:55:29
%S A213423 1,0,1,0,2,0,2,1,3,1,4,2,6,3,7,5,11,7,13,11,19,15,25,21,34,30,44,42,
%T A213423 60,56,78,78,105,103,137,139,181,186,234,246,309,323,399,425,519,554,
%U A213423 670,721,864,934,1108,1206,1425,1548,1816,1989,2318,2539,2945,3235,3738,4111,4726
%N A213423 Number of partitions of n in which all parts are >= 2 and the largest part occurs at least four times.
%F A213423 a(n) = p(n)-2*p(n-1)+p(n-3)+p(n-4)-2*p(n-6)+p(n-7), where p(n) = A000041(n).
%F A213423 G.f.: (1-x)*Product_{k>3} 1/(1-x^k).
%F A213423 a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^4 / (24*sqrt(3)*n^3). - _Vaclav Kotesovec_, Jun 02 2018
%e A213423 For n = 16 we have three partitions: {[4+4+4+4], [3+3+3+3+2+2], [2+2+2+2+2+2+2+2]}, so a(16) = 3.
%p A213423 seq(combinat:-numbpart(n)-2*combinat:-numbpart(n-1)+combinat:-numbpart(n-3)+combinat:-numbpart(n-4)-2*combinat:-numbpart(n-6)+combinat:-numbpart(n-7),n=8..70)
%Y A213423 Cf. A000041.
%K A213423 nonn
%O A213423 8,5
%A A213423 _Mircea Merca_, Jun 11 2012

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