A035698 Number of partitions of n into parts 8k+5 and 8k+7 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 3, 3, 1, 2, 1, 3, 5, 3, 6, 5, 3, 5, 3, 8, 9, 7, 11, 8, 8, 10, 9, 15, 16, 15, 19, 15, 16, 20, 19, 28, 28, 27, 33, 27, 32, 36, 36, 48, 48, 49, 55, 48, 57, 64, 65, 82, 79, 83, 92, 83, 100, 106, 112, 134, 129

Offset

1,20

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020

Mathematica

nmax = 81; s1 = Range[0, nmax/8]*8 + 5; 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 = 81; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 5)), {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-A035697, A035699-A035699.

Sequence in context: A190483 A090239 A165276 * A230204 A372646 A325592

Adjacent sequences: A035695 A035696 A035697 * A035699 A035700 A035701

Keyword

nonn

Author

Olivier Gérard

Status

approved