A035646 - OEIS

%I #16 Aug 16 2020 20:10:41

%S 0,0,0,0,1,0,1,1,1,1,4,1,4,4,4,4,10,4,11,11,11,12,22,12,25,25,26,28,

%T 45,29,52,52,55,60,87,63,101,102,108,118,160,126,187,189,202,221,285,

%U 238,333,338,363,395,492,430,574,585,629,684,828,749,964,987,1061

%N Number of partitions of n into parts 6k+2 and 6k+3 with at least one part of each type.

%H Alois P. Heinz, <a href="/A035646/b035646.txt">Table of n, a(n) for n = 1..5000</a> (first 100 terms from Robert Price)

%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 3))). - _Robert Price_, Aug 16 2020

%t nmax = 63; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 3;

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

%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 13 2020 *)

%t nmax = 63; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* _Robert Price_, Aug 16 2020 *)

%Y Cf. A035441-A035468, A035618-A035645, A035647-A035699.

%K nonn

%O 1,11

%A _Olivier Gérard_