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A239260 Number of partitions of n having (sum of odd parts) <= (sum of even parts).

%I A239260 #6 Mar 15 2014 17:17:18
%S A239260 1,0,1,1,3,2,5,7,12,11,18,26,40,40,60,83,117,120,168,230,312,331,446,
%T A239260 592,784,821,1083,1407,1826,1940,2511,3220,4097,4347,5520,6976,8779,
%U A239260 9338,11732,14627,18196,19314,23999,29654,36503,38907,47835,58555,71484,75942
%N A239260 Number of partitions of n having (sum of odd parts) <= (sum of even parts).
%H A239260 Alois P. Heinz, <a href="/A239260/b239260.txt">Table of n, a(n) for n = 0..500</a>
%F A239260 a(n) + A239262(n) = A000041(n).
%e A239260 a(8) counts these 12 partitions:  8, 62, 611, 44, 431, 422, 4211, 41111, 3221, 2222, 22211, 221111.
%t A239260 z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
%t A239260 t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
%t A239260 t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
%t A239260 t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
%t A239260 t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
%t A239260 t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
%t A239260 (* _Peter J. C. Moses_, Mar 12 2014 *)
%Y A239260 Cf. A239259, A239261, A239262, A239263, A000041.
%K A239260 nonn,easy
%O A239260 0,5
%A A239260 _Clark Kimberling_, Mar 13 2014