A015755 Number of partitions of n into distinct parts, none being 8.

1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 13, 15, 18, 22, 27, 31, 37, 44, 51, 61, 71, 82, 95, 111, 128, 148, 171, 195, 225, 258, 295, 337, 384, 437, 497, 565, 639, 724, 818, 923, 1042, 1173, 1319, 1483, 1665, 1866, 2092, 2341, 2616, 2924, 3263, 3637, 4053, 4512, 5016

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A025147, A015744, A015745, A015746, A015750, A015753, A015754.

Programs

Mathematica

CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^8), {q, 0, 60}], q]
Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 8]], {n, 0, 56}] (* Robert Price, May 18 2020 *)

Formula

a(n) = A015743(n+8). - Michel Marcus, Feb 20 2014

a(n) = A000009(n) - a(n-8) for n >= 0, a(n) = 0 otherwise. - Yuchun Ji, Dec 25 2018

Extensions

Corrected and extended by Dean Hickerson, Oct 10 2001