A035689 Number of partitions of n into parts 8k+2 and 8k+7 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 4, 3, 7, 3, 8, 3, 8, 4, 10, 8, 14, 9, 16, 9, 18, 11, 22, 17, 28, 19, 32, 21, 36, 25, 44, 35, 52, 40, 60, 44, 68, 52, 82, 66, 95, 76, 108, 85, 123, 100, 145, 122, 166, 140, 188, 157, 214, 182, 250, 215, 283, 245

Offset

1,17

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 + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 15 2020

Mathematica

nmax = 74; s1 = Range[0, nmax/8]*8 + 2; 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 15 2020 *)
nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035688, A035690-A035699.

Sequence in context: A362720 A205526 A233269 * A296082 A294786 A294787

Adjacent sequences: A035686 A035687 A035688 * A035690 A035691 A035692

Keyword

nonn

Author

Olivier Gérard

Status

approved