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%I #17 Aug 17 2020 07:29:41
%S 0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,3,1,0,3,1,0,3,1,6,3,1,7,3,1,7,3,
%T 12,7,3,15,7,3,16,7,21,16,7,28,16,7,31,16,36,32,16,50,32,16,57,32,60,
%U 60,32,85,61,32,100,61,98,107,61,141,110,61,169,111,157,184,111,226
%N Number of partitions of n into parts 8k and 8k+3 with at least one part of each type.
%H Robert Price, <a href="/A035674/b035674.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 3)))*(-1 + 1/Product_{k>=1} (1 - x^(8*k))). - _Robert Price_, Aug 12 2020
%t nmax = 78; s1 = Range[1, nmax/8]*8; s2 = Range[0, nmax/8]*8 + 3;
%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 12 2020 *)
%t nmax = 78; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 12 2020 *)
%Y Cf. A035441-A035468, A035618-A035673, A035675-A035699.
%K nonn
%O 1,19
%A _Olivier Gérard_
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