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%I #15 Aug 16 2020 18:37:41
%S 0,0,0,0,0,0,0,1,0,1,0,1,0,4,0,4,0,4,0,10,0,11,0,11,0,22,0,25,0,26,0,
%T 44,0,51,0,54,0,84,0,98,0,105,0,152,0,178,0,193,0,266,0,312,0,341,0,
%U 452,0,528,0,581,0,749,0,873,0,964,0,1214,0,1409,0,1561,0,1930,0,2234
%N Number of partitions of n into parts 6k and 6k+2 with at least one part of each type.
%H Robert Price, <a href="/A035638/b035638.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - _Robert Price_, Aug 12 2020
%t nmax = 76; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 2;
%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 = 76; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 12 2020 *)
%Y Cf. A035441-A035468, A035618-A035637, A035639-A035699.
%K nonn
%O 1,14
%A _Olivier Gérard_
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