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%I #14 Aug 16 2020 15:32:29
%S 0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,3,1,1,0,3,3,1,1,6,3,3,1,8,7,3,3,12,9,
%T 7,3,16,15,9,7,22,19,16,9,30,29,20,16,40,38,32,20,54,54,41,33,69,70,
%U 61,42,93,95,78,64,118,124,110,81,157,163,141,117,196,211,192,149,258
%N Number of partitions of n into parts 8k+4 and 8k+5 with at least one part of each type.
%H Robert Price, <a href="/A035694/b035694.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5))). - _Robert Price_, Aug 16 2020
%t nmax = 77; s1 = Range[0, nmax/8]*8 + 4; s2 = Range[0, nmax/8]*8 + 5;
%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 16 2020 *)
%t nmax = 77; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y Cf. A035441-A035468, A035618-A035693, A035695-A035699.
%K nonn
%O 1,17
%A _Olivier Gérard_
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