A035452 - OEIS

%I #13 Aug 04 2020 08:45:31

%S 1,1,1,1,1,2,2,2,3,3,3,4,4,5,6,6,7,9,9,10,11,12,14,16,17,19,21,23,25,

%T 28,31,34,37,41,44,49,53,57,63,69,74,82,88,95,104,112,121,133,142,154,

%U 167,179,193,209,224,243,261,280,301,324,347,373,400,430,460,494,528

%N Number of partitions of n into parts 8k+1 or 8k+6.

%H Robert Price, <a href="/A035452/b035452.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) * Gamma(1/8) / (4 * 2^(15/16) * 3^(3/16) * Pi^(9/8) * n^(11/16)). - _Vaclav Kotesovec_, Aug 26 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+6))), {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 + 1}~Join~{Range[0, kmax]*8 + 6}];

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

%Y Cf. A035683.

%K nonn

%O 1,6

%A _Olivier Gérard_