A015745 Number of partitions of n into distinct parts, none being 3.

1, 1, 1, 1, 1, 2, 3, 4, 4, 5, 6, 8, 10, 12, 14, 17, 20, 24, 29, 34, 40, 47, 55, 64, 75, 87, 101, 117, 135, 155, 179, 205, 235, 269, 307, 350, 399, 453, 514, 583, 660, 746, 843, 950, 1070, 1205, 1354, 1520, 1705, 1910, 2138, 2392, 2672, 2982, 3326, 3706, 4126

Offset

0,6

Links

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

Formula

a(n) = A015737(n+3). - Michel Marcus, Feb 20 2014

a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Oct 30 2015

Mathematica

CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^3), {q, 0, 60}], q]
Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 3]], {n, 0, 56}] (* Robert Price, May 17 2020 *)

Crossrefs

Cf. A025147, A015744, A015746, A015750, A015753, A015754, A015755.

Sequence in context: A049877 A029063 A015737 * A017854 A261171 A330264

Adjacent sequences: A015742 A015743 A015744 * A015746 A015747 A015748

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected and extended by Dean Hickerson, Oct 10, 2001

Status

approved