A035699 Number of partitions of n into parts 8k+6 and 8k+7 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 3, 2, 3, 0, 1, 1, 3, 3, 6, 4, 5, 1, 3, 3, 7, 7, 11, 7, 8, 3, 7, 8, 15, 13, 19, 12, 13, 8, 16, 17, 27, 24, 30, 20, 23, 18, 32, 32, 46, 40, 48, 34, 41, 37, 56, 57, 76, 66, 76, 58, 71, 67, 97, 96, 122, 105, 119

Offset

1,21

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020

Mathematica

nmax = 83; s1 = Range[0, nmax/8]*8 + 6; s2 = Range[0, nmax/8]*8 + 7;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 16 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035698.

Sequence in context: A284264 A273302 A025086 * A132406 A197881 A332712

Adjacent sequences: A035696 A035697 A035698 * A035700 A035701 A035702

Keyword

nonn

Author

Olivier Gérard

Status

approved