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 A035443 Number of partitions of n into parts 8k or 8k+3. 1

%I

%S 0,0,1,0,0,1,0,1,1,0,2,1,0,2,1,2,2,1,4,2,1,5,2,4,5,2,8,5,2,10,5,7,11,

%T 5,14,11,5,19,11,12,21,11,24,22,11,33,22,22,38,22,41,40,22,58,41,37,

%U 68,41,67,73,41,95,75,63,114,76,108,124,76,155,129,106,188,131,173

%N Number of partitions of n into parts 8k or 8k+3.

%H Robert Price, <a href="/A035443/b035443.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/8) / (4 * 2^(3/16) * 3^(7/16) * Pi^(5/8) * n^(15/16)). - _Vaclav Kotesovec_, Aug 26 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)

%t nmax = 50; kmax = nmax/8;

%t s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 3}];

%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)

%Y Cf. A035674.

%K nonn

%O 1,11