A035684 Number of partitions of n into parts 8k+1 and 8k+7 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 4, 4, 4, 4, 4, 4, 5, 7, 10, 11, 11, 11, 11, 12, 14, 18, 23, 25, 26, 26, 27, 29, 33, 40, 47, 52, 54, 56, 58, 62, 70, 81, 93, 101, 107, 111, 116, 124, 137, 155, 172, 188, 199, 208, 218, 233, 255, 282, 311, 336, 357, 374, 393

Offset

1,15

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 + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7). - Robert Price, Aug 15 2020

Mathematica

nmax = 68; s1 = Range[0, nmax/8]*8 + 1; 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 15 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035683, A035685-A035699.

Sequence in context: A040002 A151798 A334897 * A049111 A096509 A035661

Adjacent sequences: A035681 A035682 A035683 * A035685 A035686 A035687

Keyword

nonn

Author

Olivier Gérard

Status

approved