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

1,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A066897.

Sequence in context: A278504 A085179 A113782 * A125675 A301501 A072787

Adjacent sequences: A090865 A090866 A090867 * A090869 A090870 A090871

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 12 2004

Extensions

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

Status

approved