A035697 Number of partitions of n into parts 8k+5 and 8k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 1, 4, 1, 3, 2, 3, 5, 5, 3, 7, 3, 7, 6, 7, 9, 10, 7, 13, 8, 14, 12, 15, 17, 19, 15, 23, 17, 27, 24, 28, 30, 34, 30, 41, 33, 48, 43, 51, 53, 59, 55, 70, 61, 83, 76, 89, 89, 100, 97, 118, 108, 138, 127, 149

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^(8 k + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 16 2020

Mathematica

nmax = 79; s1 = Range[0, nmax/8]*8 + 5; 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 16 2020 *)
nmax = 79; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035696, A035698-A035699.

Sequence in context: A051159 A331545 A349465 * A135549 A262666 A124737

Adjacent sequences: A035694 A035695 A035696 * A035698 A035699 A035700

Keyword

nonn

Author

Olivier Gérard

Status

approved