A035655 Number of partitions of n into parts 7k and 7k+5 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 1, 0, 3, 0, 6, 1, 0, 3, 0, 7, 1, 11, 3, 0, 7, 1, 14, 3, 18, 7, 1, 15, 3, 25, 7, 30, 15, 3, 28, 7, 44, 15, 47, 29, 7, 51, 15, 72, 29, 73, 54, 15, 87, 29, 116, 55, 111, 94, 29, 144, 55, 180, 97, 167, 159, 55, 230, 98, 276

Offset

1,19

Links

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

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - Robert Price, Aug 12 2020

Mathematica

nmax = 80; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 80; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035654, A035656-A035699.

Sequence in context: A171913 A342154 A074936 * A353323 A239446 A036857

Adjacent sequences: A035652 A035653 A035654 * A035656 A035657 A035658

Keyword

nonn

Author

Olivier Gérard

Status

approved