|
%I #11 Aug 04 2020 12:16:02
%S 0,1,0,1,0,1,1,1,1,2,1,2,1,3,2,3,3,4,3,5,4,6,5,7,7,8,8,10,9,13,11,15,
%T 14,17,17,20,20,24,23,29,28,33,33,38,39,45,45,53,53,61,62,70,72,81,83,
%U 95,96,108,111,124,128,142,147,164,168,187,193,212,221,242,252,277
%N Number of partitions of n into parts 8k+2 or 8k+7.
%H Robert Price, <a href="/A035458/b035458.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(7/8) * Gamma(1/4) / (4 * 2^(9/16) * 3^(5/16) * Pi^(7/8) * n^(13/16)). - _Vaclav Kotesovec_, Aug 26 2015
%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+7))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t nmax = 60; kmax = nmax/8;
%t s = Flatten[{Range[0, kmax]*8 + 2}~Join~{Range[0, kmax]*8 + 7}];
%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 04 2020 *)
%K nonn
%O 1,10
%A _Olivier Gérard_
|
