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%I #10 Aug 16 2020 15:38:00
%S 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,2,0,0,0,1,1,3,2,3,0,1,1,3,3,
%T 6,4,5,1,3,3,7,7,11,7,8,3,7,8,15,13,19,12,13,8,16,17,27,24,30,20,23,
%U 18,32,32,46,40,48,34,41,37,56,57,76,66,76,58,71,67,97,96,122,105,119
%N Number of partitions of n into parts 8k+6 and 8k+7 with at least one part of each type.
%H Robert Price, <a href="/A035699/b035699.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - _Robert Price_, Aug 16 2020
%t nmax = 83; s1 = Range[0, nmax/8]*8 + 6; s2 = Range[0, nmax/8]*8 + 7;
%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 + 6)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y Cf. A035441-A035468, A035618-A035698.
%K nonn
%O 1,21
%A _Olivier Gérard_
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