A035692 - OEIS

%I #11 Aug 16 2020 14:08:49

%S 0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,0,2,2,0,2,3,0,4,3,3,4,4,4,6,4,8,6,9,9,

%T 8,11,13,8,19,14,15,21,18,19,30,19,32,32,29,38,41,36,53,43,56,59,59,

%U 67,75,70,93,81,102,105,105,122,133,123,165,145,170,189,183,203,237

%N Number of partitions of n into parts 8k+3 and 8k+6 with at least one part of each type.

%H Robert Price, <a href="/A035692/b035692.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - _Robert Price_, Aug 15 2020

%t nmax = 75; s1 = Range[0, nmax/8]*8 + 3; s2 = Range[0, nmax/8]*8 + 6;

%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],

%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)

%t nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* _Robert Price_, Aug 15 2020*)

%Y Cf. A035441-A035468, A035618-A035691, A035693-A035699.

%K nonn

%O 1,15

%A _Olivier Gérard_