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%I #21 Aug 16 2020 16:34:19
%S 0,0,0,0,1,0,1,1,3,1,4,3,7,4,10,8,15,11,21,18,30,24,42,37,56,50,78,70,
%T 102,95,137,129,179,171,236,227,303,297,395,386,502,501,643,641,814,
%U 820,1030,1041,1291,1317,1622,1652,2018,2075,2509,2582,3107,3212,3834
%N Number of partitions of n into parts 4k+2 and 4k+3 with at least one part of each type.
%H Alois P. Heinz, <a href="/A035626/b035626.txt">Table of n, a(n) for n = 1..5000</a> (first 100 terms from Robert Price)
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(4 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(4 k + 3))). - _Robert Price_, Aug 16 2020
%t nmax = 59; s1 = Range[0, nmax/4]*4 + 2; s2 = Range[0, nmax/4]*4 + 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 = 59; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(4 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(4 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y Bisection of A035695 (even part).
%Y Cf. A035441-A035468, A035618-A035625, A035627-A035699.
%K nonn
%O 1,9
%A _Olivier Gérard_
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