A035696 Number of partitions of n into parts 8k+4 and 8k+7 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 3, 0, 0, 1, 3, 0, 1, 3, 6, 0, 1, 3, 7, 1, 3, 7, 11, 1, 3, 8, 14, 3, 7, 14, 20, 3, 8, 17, 26, 7, 15, 27, 34, 8, 18, 34, 45, 15, 30, 48, 57, 18, 37, 61, 75, 31, 55, 83, 94, 38, 69, 106, 123, 58, 98, 139, 152, 72, 123, 177, 197, 105

Offset

1,19

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 + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020

Mathematica

nmax = 80; s1 = Range[0, nmax/8]*8 + 4; 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 16 2020 *)
nmax = 80; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035695, A035697-A035699.

Sequence in context: A280815 A165974 A090622 * A170840 A300725 A035630

Adjacent sequences: A035693 A035694 A035695 * A035697 A035698 A035699

Keyword

nonn

Author

Olivier Gérard

Status

approved