A035687 Number of partitions of n into parts 8k+2 and 8k+5 with at least one part of each type.

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, 12, 21, 12, 25, 18, 26, 24, 31, 28, 42, 29, 50, 38, 55, 50, 62, 58, 79, 63, 95, 76, 105, 96, 118, 113, 144, 123, 172, 145, 193, 178, 213, 208, 255, 230, 302, 262, 340, 316

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..5000

Crossrefs

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

Programs

Mathematica

nmax = 70; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
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*)

Formula

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