A035670 Number of partitions of n into parts 7k+4 and 7k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 2, 2, 4, 2, 2, 2, 6, 4, 6, 6, 6, 4, 8, 10, 10, 10, 13, 11, 12, 14, 21, 18, 21, 21, 25, 22, 30, 34, 37, 35, 41, 42, 46, 50, 63, 61, 66, 67, 79, 78, 93, 100, 110, 107, 120, 128, 141, 149, 172, 175, 186, 192, 220, 226

Offset

1,17

Links

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

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 6). - Robert Price, Aug 15 2020

Mathematica

nmax = 75; s1 = Range[0, nmax/7]*7 + 4; 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 = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 4)), {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-A035669, A035671-A035699.

Sequence in context: A329972 A321005 A055254 * A058839 A275946 A287824

Adjacent sequences: A035667 A035668 A035669 * A035671 A035672 A035673

Keyword

nonn

Author

Olivier Gérard

Status

approved