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

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

Corrected and extended by Dean Hickerson, Oct 10 2001