A035646 Number of partitions of n into parts 6k+2 and 6k+3 with at least one part of each type.

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, 45, 29, 52, 52, 55, 60, 87, 63, 101, 102, 108, 118, 160, 126, 187, 189, 202, 221, 285, 238, 333, 338, 363, 395, 492, 430, 574, 585, 629, 684, 828, 749, 964, 987, 1061

Offset

1,11

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)

Formula

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

Mathematica

nmax = 63; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
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 *)

Crossrefs

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

Sequence in context: A117445 A145079 A196222 * A144034 A366887 A204714

Adjacent sequences: A035643 A035644 A035645 * A035647 A035648 A035649

Keyword

nonn

Author

Olivier Gérard

Status

approved