A035688 Number of partitions of n into parts 8k+2 and 8k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 4, 0, 4, 0, 5, 0, 7, 0, 10, 0, 12, 0, 14, 0, 18, 0, 24, 0, 28, 0, 33, 0, 41, 0, 50, 0, 59, 0, 70, 0, 84, 0, 100, 0, 117, 0, 137, 0, 161, 0, 188, 0, 219, 0, 254, 0, 295, 0, 341, 0, 393, 0, 453, 0, 520, 0, 595, 0, 682, 0, 780, 0, 889, 0

Offset

1,14

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 15 2020

Mathematica

nmax = 79; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 79; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035687, A035689-A035699.

Sequence in context: A302826 A332903 A082519 * A364105 A046769 A145893

Adjacent sequences: A035685 A035686 A035687 * A035689 A035690 A035691

Keyword

nonn

Author

Olivier Gérard

Status

approved