A035681 Number of partitions of n into parts 8k+1 and 8k+4 with at least one part of each type.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 5, 5, 8, 8, 8, 8, 14, 15, 15, 15, 22, 23, 23, 23, 34, 37, 38, 38, 51, 54, 55, 55, 74, 81, 84, 85, 108, 116, 119, 120, 151, 165, 172, 175, 214, 230, 238, 241, 291, 317, 332, 339, 402, 434, 451, 459, 538, 584, 613, 628, 727, 784

Offset

1,9

Links

Robert Price, 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 + 4). - Robert Price, Aug 15 2020

Mathematica

nmax = 66; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035680, A035682-A035699.

Sequence in context: A118486 A288026 A141299 * A195601 A352723 A222255

Adjacent sequences: A035678 A035679 A035680 * A035682 A035683 A035684

Keyword

nonn

Author

Olivier Gérard

Status

approved