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%I #15 Aug 16 2020 18:43:17
%S 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,0,0,0,1,3,6,0,0,1,3,7,11,0,1,3,7,
%T 14,18,1,3,7,15,25,30,3,7,15,28,44,47,7,15,29,51,72,73,15,29,54,87,
%U 116,111,29,55,94,144,180,167,55,97,159,230,276,249,98,166,259,360
%N Number of partitions of n into parts 6k and 6k+5 with at least one part of each type.
%H Robert Price, <a href="/A035641/b035641.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - _Robert Price_, Aug 12 2020
%t nmax = 75; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 5;
%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 = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 12 2020 *)
%Y Cf. A035441-A035468, A035618-A035640, A035642-A035699.
%K nonn
%O 1,17
%A _Olivier Gérard_
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