A035676 Number of partitions of n into parts 8k and 8k+5 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, 1, 0, 0, 3, 0, 1, 0, 0, 3, 0, 1, 6, 0, 3, 0, 1, 7, 0, 3, 11, 1, 7, 0, 3, 14, 1, 7, 18, 3, 15, 1, 7, 25, 3, 15, 30, 7, 28, 3, 15, 44, 7, 29, 47, 15, 51, 7, 29, 72, 15, 54, 73, 29, 87, 15, 55, 116, 29, 94, 111, 55, 144, 29, 97, 180, 55

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 + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(8*k))). - Robert Price, Aug 13 2020

Mathematica

nmax = 83; s1 = Range[1, nmax/8]*8; 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 13 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 13 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035675, A035677-A035699.

Sequence in context: A051830 A356098 A106216 * A369283 A129685 A292835

Adjacent sequences: A035673 A035674 A035675 * A035677 A035678 A035679

Keyword

nonn

Author

Olivier Gérard

Status

approved