A213423 - OEIS

%I #15 Jun 02 2018 06:55:29

%S 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 60,56,78,78,105,103,137,139,181,186,234,246,309,323,399,425,519,554,

%U 670,721,864,934,1108,1206,1425,1548,1816,1989,2318,2539,2945,3235,3738,4111,4726

%N Number of partitions of n in which all parts are >= 2 and the largest part occurs at least four times.

%F 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 G.f.: (1-x)*Product_{k>3} 1/(1-x^k).

%F a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^4 / (24*sqrt(3)*n^3). - _Vaclav Kotesovec_, Jun 02 2018

%e 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 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 Cf. A000041.

%K nonn

%O 8,5

%A _Mircea Merca_, Jun 11 2012