cp's OEIS Frontend

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

%I A090868 #14 May 28 2018 05:29:00
%S A090868 1,1,3,2,6,5,11,8,20,15,32,24,51,39,80,58,119,90,175,130,255,190,361,
%T A090868 268,508,379,706,522,967,722,1313,974,1771,1317,2363,1754,3131,2330,
%U A090868 4123,3058,5388,4010,7001,5200,9053,6731,11631,8642,14878,11068,18944,14076
%N A090868 Number of partitions of n such that the set of odd parts has only one element.
%H A090868 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 A090868 G.f.: Sum_{m>0} x^(2*m-1)/(1-x^(2*m-1))/Product_{m>0} (1-x^(2*m)).
%p A090868 b:= proc(n, i, t) option remember; `if`(n=0, `if`(t, 1, 0),
%p A090868       `if`(i<1, 0, add(b(n-i*j, i-1, t or j>0 and i::odd),
%p A090868        j=0..`if`(t and i::odd, 0, n/i))))
%p A090868     end:
%p A090868 a:= n-> b(n$2, false):
%p A090868 seq(a(n), n=1..60);  # _Alois P. Heinz_, Jun 30 2016
%t A090868 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 A090868 Cf. A066897.
%K A090868 easy,nonn
%O A090868 1,3
%A A090868 _Vladeta Jovovic_, Feb 12 2004
%E A090868 More terms from _Robert G. Wilson v_, Feb 16 2004