A035452 Number of partitions of n into parts 8k+1 or 8k+6.

1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 9, 10, 11, 12, 14, 16, 17, 19, 21, 23, 25, 28, 31, 34, 37, 41, 44, 49, 53, 57, 63, 69, 74, 82, 88, 95, 104, 112, 121, 133, 142, 154, 167, 179, 193, 209, 224, 243, 261, 280, 301, 324, 347, 373, 400, 430, 460, 494, 528

Offset

1,6

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) * Gamma(1/8) / (4 * 2^(15/16) * 3^(3/16) * Pi^(9/8) * n^(11/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 6}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Cf. A035683.

Sequence in context: A025771 A154403 A053265 * A199575 A120187 A029062

Adjacent sequences: A035449 A035450 A035451 * A035453 A035454 A035455

Keyword

nonn

Author

Olivier Gérard

Status

approved