A035668 Number of partitions of n into parts 7k+3 and 7k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 3, 4, 3, 3, 4, 4, 4, 6, 8, 8, 6, 9, 11, 8, 13, 18, 13, 14, 21, 19, 18, 29, 30, 25, 32, 38, 35, 40, 51, 52, 50, 59, 66, 67, 73, 89, 93, 89, 104, 119, 115, 129, 156, 154, 153, 186, 195, 195, 228, 254, 251, 269, 304, 319

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^(7 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 6)). - Robert Price, Aug 15 2020

Mathematica

nmax = 74; s1 = Range[0, nmax/7]*7 + 3; s2 = Range[0, nmax/7]*7 + 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 = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035667, A035669-A035699.

Sequence in context: A109265 A184334 A225399 * A307757 A215283 A066518

Adjacent sequences: A035665 A035666 A035667 * A035669 A035670 A035671

Keyword

nonn

Author

Olivier Gérard

Status

approved