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%I #21 Aug 16 2020 17:05:59
%S 0,0,0,0,0,0,0,1,0,0,1,0,3,1,0,3,1,6,3,1,7,3,12,7,3,15,7,21,16,7,28,
%T 16,36,31,16,50,32,60,57,32,85,60,98,100,61,141,107,157,169,110,226,
%U 184,249,276,191,358,305,388,442,320,554,495,598,691,524,848,782,911
%N Number of partitions of n into parts 5k and 5k+3 with at least one part of each type.
%H Robert Price, <a href="/A035629/b035629.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+3)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - _Robert Price_, Aug 06 2020
%t nmax = 68; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 3;
%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 06 2020 *)
%Y Cf. A035441-A035468, A035618-A035628, A035630-A035699.
%K nonn
%O 1,13
%A _Olivier Gérard_
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