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

0,4

Links

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

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

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 *)

Crossrefs

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

Sequence in context: A325096 A261771 A015743 * A096443 A126442 A129306

Adjacent sequences: A015752 A015753 A015754 * A015756 A015757 A015758

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected and extended by Dean Hickerson, Oct 10 2001

Status

approved