A035687 - OEIS

%I #13 Aug 15 2020 23:14:33

%S 0,0,0,0,0,0,1,0,1,0,1,1,1,1,3,1,4,1,4,3,4,4,7,4,10,4,11,8,11,11,15,

%T 12,21,12,25,18,26,24,31,28,42,29,50,38,55,50,62,58,79,63,95,76,105,

%U 96,118,113,144,123,172,145,193,178,213,208,255,230,302,262,340,316

%N Number of partitions of n into parts 8k+2 and 8k+5 with at least one part of each type.

%H Alois P. Heinz, <a href="/A035687/b035687.txt">Table of n, a(n) for n = 1..5000</a>

%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5))). - _Robert Price_, Aug 15 2020

%t nmax = 70; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 5;

%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 = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* _Robert Price_, Aug 15 2020*)

%Y Cf. A035441-A035468, A035618-A035686, A035688-A035699.

%K nonn

%O 1,15

%A _Olivier Gérard_