A035692 Number of partitions of n into parts 8k+3 and 8k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 3, 0, 4, 3, 3, 4, 4, 4, 6, 4, 8, 6, 9, 9, 8, 11, 13, 8, 19, 14, 15, 21, 18, 19, 30, 19, 32, 32, 29, 38, 41, 36, 53, 43, 56, 59, 59, 67, 75, 70, 93, 81, 102, 105, 105, 122, 133, 123, 165, 145, 170, 189, 183, 203, 237

Offset

1,15

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 15 2020

Mathematica

nmax = 75; s1 = Range[0, nmax/8]*8 + 3; 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 = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 3)), {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-A035691, A035693-A035699.

Sequence in context: A318734 A029317 A127800 * A308654 A329860 A334209

Adjacent sequences: A035689 A035690 A035691 * A035693 A035694 A035695

Keyword

nonn

Author

Olivier Gérard

Status

approved