A090868 - OEIS

%I #14 May 28 2018 05:29:00

%S 1,1,3,2,6,5,11,8,20,15,32,24,51,39,80,58,119,90,175,130,255,190,361,

%T 268,508,379,706,522,967,722,1313,974,1771,1317,2363,1754,3131,2330,

%U 4123,3058,5388,4010,7001,5200,9053,6731,11631,8642,14878,11068,18944,14076

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

%H Vaclav Kotesovec, <a href="/A090868/b090868.txt">Table of n, a(n) for n = 1..14572</a> (terms 1..5000 from Alois P. Heinz)

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

%p b:= proc(n, i, t) option remember; `if`(n=0, `if`(t, 1, 0),

%p       `if`(i<1, 0, add(b(n-i*j, i-1, t or j>0 and i::odd),

%p        j=0..`if`(t and i::odd, 0, n/i))))

%p     end:

%p a:= n-> b(n$2, false):

%p seq(a(n), n=1..60);  # _Alois P. Heinz_, Jun 30 2016

%t 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 *)

%Y Cf. A066897.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Feb 12 2004

%E More terms from _Robert G. Wilson v_, Feb 16 2004