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%I #10 Aug 16 2020 15:31:56
%S 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,2,0,1,1,1,2,2,1,4,1,3,2,3,5,5,3,
%T 7,3,7,6,7,9,10,7,13,8,14,12,15,17,19,15,23,17,27,24,28,30,34,30,41,
%U 33,48,43,51,53,59,55,70,61,83,76,89,89,100,97,118,108,138,127,149
%N Number of partitions of n into parts 8k+5 and 8k+6 with at least one part of each type.
%H Robert Price, <a href="/A035697/b035697.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - _Robert Price_, Aug 16 2020
%t nmax = 79; s1 = Range[0, nmax/8]*8 + 5; 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 = 79; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y Cf. A035441-A035468, A035618-A035696, A035698-A035699.
%K nonn
%O 1,19
%A _Olivier Gérard_
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