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%I #15 Aug 16 2020 21:18:35
%S 0,0,0,0,1,0,1,1,1,1,2,3,2,4,4,4,5,6,8,7,11,11,12,14,16,19,19,25,26,
%T 29,32,37,41,43,53,56,61,69,77,83,90,106,110,123,135,149,160,176,197,
%U 210,231,253,276,297,323,359,381,418,453,494,526,576,627,669,728,790
%N Number of partitions of n into parts 7k+2 and 7k+3 with at least one part of each type.
%H Alois P. Heinz, <a href="/A035662/b035662.txt">Table of n, a(n) for n = 1..1000</a> (first 125 terms from Robert Price)
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 3))). - _Robert Price_, Aug 16 2020
%t nmax = 66; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 3;
%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 14 2020 *)
%t nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y Cf. A035441-A035468, A035618-A035661, A035663-A035699.
%K nonn
%O 1,11
%A _Olivier Gérard_
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