A035682 Number of partitions of n into parts 8k+1 and 8k+5 with at least one part of each type.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 5, 5, 5, 7, 7, 8, 11, 12, 14, 14, 15, 19, 20, 22, 26, 29, 34, 35, 37, 43, 46, 51, 57, 63, 72, 76, 81, 91, 98, 107, 117, 128, 144, 153, 163, 179, 192, 210, 226, 245, 272, 290, 310, 336, 360, 391, 418, 450, 494, 527, 564, 605

Offset

1,11

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(8 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5). - Robert Price, Aug 15 2020

Mathematica

nmax = 67; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035681, A035683-A035699.

Sequence in context: A275433 A096323 A282562 * A054543 A240861 A029046

Adjacent sequences: A035679 A035680 A035681 * A035683 A035684 A035685

Keyword

nonn

Author

Olivier Gérard

Status

approved