A035641 Number of partitions of n into parts 6k and 6k+5 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 1, 3, 6, 0, 0, 1, 3, 7, 11, 0, 1, 3, 7, 14, 18, 1, 3, 7, 15, 25, 30, 3, 7, 15, 28, 44, 47, 7, 15, 29, 51, 72, 73, 15, 29, 54, 87, 116, 111, 29, 55, 94, 144, 180, 167, 55, 97, 159, 230, 276, 249, 98, 166, 259, 360

Offset

1,17

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020

Mathematica

nmax = 75; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035640, A035642-A035699.

Sequence in context: A218788 A328969 A027185 * A242434 A036873 A081130

Adjacent sequences: A035638 A035639 A035640 * A035642 A035643 A035644

Keyword

nonn

Author

Olivier Gérard

Status

approved