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%I #14 Aug 16 2020 15:33:46
%S 0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,3,0,1,0,4,0,3,0,7,0,4,0,10,0,8,0,
%T 15,0,11,0,21,0,18,0,30,0,24,0,42,0,37,0,56,0,50,0,78,0,70,0,102,0,95,
%U 0,137,0,129,0,179,0,171,0,236,0,227,0,303,0,297,0,395,0,386,0,502,0
%N Number of partitions of n into parts 8k+4 and 8k+6 with at least one part of each type.
%H Alois P. Heinz, <a href="/A035695/b035695.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - _Robert Price_, Aug 16 2020
%t nmax = 83; s1 = Range[0, nmax/8]*8 + 4; s2 = Range[0, nmax/8]*8 + 6;
%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 = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y Bisections give A035626 (even part), A000004 (odd part).
%Y Cf. A035441-A035468, A035618-A035694, A035696-A035699.
%K nonn
%O 1,18
%A _Olivier Gérard_
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