A090868 Number of partitions of n such that the set of odd parts has only one element.

1, 1, 3, 2, 6, 5, 11, 8, 20, 15, 32, 24, 51, 39, 80, 58, 119, 90, 175, 130, 255, 190, 361, 268, 508, 379, 706, 522, 967, 722, 1313, 974, 1771, 1317, 2363, 1754, 3131, 2330, 4123, 3058, 5388, 4010, 7001, 5200, 9053, 6731, 11631, 8642, 14878, 11068, 18944, 14076

Offset: 1

Author

Vladeta Jovovic, Feb 12 2004

Keywords

• easy
• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..14572 (terms 1..5000 from Alois P. Heinz)

Crossrefs

Cf. A066897.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t, 1, 0),
      `if`(i<1, 0, add(b(n-i*j, i-1, t or j>0 and i::odd),
       j=0..`if`(t and i::odd, 0, n/i))))
    end:
a:= n-> b(n$2, false):
seq(a(n), n=1..60);  # Alois P. Heinz, Jun 30 2016

Mathematica

first Needs["DiscreteMath`Combinatorica`"], then f[n_] := Count[ Plus @@@ Mod[ Union /@ Partitions[n], 2], 1]; Table[ f[n], {n, 1, 51}] (* Robert G. Wilson v, Feb 16 2004 *)

Formula

G.f.: Sum_{m>0} x^(2*m-1)/(1-x^(2*m-1))/Product_{m>0} (1-x^(2*m)).

Extensions

More terms from Robert G. Wilson v, Feb 16 2004