cp's OEIS Frontend

A219607 Number of partitions of n into distinct parts 5*k+2 or 5*k+3.

%I A219607 #20 Mar 20 2017 07:45:36
%S A219607 1,0,1,1,0,1,0,1,1,1,2,1,2,2,1,3,1,3,3,2,5,3,5,5,4,7,4,7,7,6,11,7,11,
%T A219607 11,9,15,10,15,16,14,22,16,23,23,20,30,22,31,32,29,42,33,44,45,41,56,
%U A219607 45,59,61,57,78,64,82,84,78,103,86,108,112,107,138
%N A219607 Number of partitions of n into distinct parts 5*k+2 or 5*k+3.
%C A219607 Convolution of A281271 and A281272. - _Vaclav Kotesovec_, Jan 18 2017
%H A219607 Seiichi Manyama, <a href="/A219607/b219607.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..250 from Reinhard Zumkeller)
%F A219607 a(n) ~ exp(sqrt(2*n/15)*Pi) / (2*30^(1/4)*n^(3/4)) * (1 - (3*sqrt(15/2)/(8*Pi) + 11*Pi/(60*sqrt(30))) / sqrt(n)). - _Vaclav Kotesovec_, Jan 18 2017, extended Jan 24 2017
%e A219607 a(10) = #{8+2, 7+3} = 2;
%e A219607 a(11) = #{8+3} = 1;
%e A219607 a(12) = #{12, 7+3+2} = 2;
%e A219607 a(13) = #{13, 8+3+2} = 2;
%e A219607 a(14) = #{12+2} = 1;
%e A219607 a(15) = #{13+2, 12+3, 8+7} = 3;
%e A219607 a(16) = #{13+3} = 1;
%e A219607 a(17) = #{17, 12+3+2, 8+7+2} = 3;
%e A219607 a(18) = #{18, 13+3+2, 8+7+3} = 3;
%e A219607 a(19) = #{17+2, 12+7} = 2;
%e A219607 a(20) = #{18+2, 17+3, 13+7, 12+8, 8+7+3+2} = 5.
%t A219607 nmax = 100; CoefficientList[Series[Product[(1 + x^(5*k - 2))*(1 + x^(5*k - 3)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jan 18 2017 *)
%o A219607 (Haskell)
%o A219607 a219607 = p a047221_list where
%o A219607    p _      0 = 1
%o A219607    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%Y A219607 Cf. A047221, A003106, A203776.
%K A219607 nonn
%O A219607 0,11
%A A219607 _Reinhard Zumkeller_, Nov 30 2012