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A090868 Number of partitions of n such that the set of odd parts has only one element. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)