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%I #15 Aug 16 2020 20:49:43
%S 0,0,0,0,0,1,1,1,1,1,2,2,4,4,4,5,5,7,7,10,12,12,14,14,18,20,24,28,29,
%T 33,35,41,45,51,59,63,71,75,85,94,104,118,126,140,150,166,182,198,222,
%U 239,263,282,308,337,364,403,433,473,508,550,599,643,705,758,823,884
%N Number of partitions of n into parts 7k+1 and 7k+5 with at least one part of each type.
%H Alois P. Heinz, <a href="/A035660/b035660.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 + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 5))). - _Robert Price_, Aug 16 2020
%t nmax = 66; s1 = Range[0, nmax/7]*7 + 1; s2 = Range[0, nmax/7]*7 + 5;
%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 + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y Cf. A035441-A035468, A035618-A035659, A035661-A035699.
%K nonn
%O 1,11
%A _Olivier Gérard_
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