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A239263 Number of partitions of n having (sum of odd parts) >= (sum of even parts).

%I A239263 #8 Mar 15 2014 16:58:01
%S A239263 1,1,1,2,3,5,6,8,14,19,24,30,49,61,75,93,144,177,217,260,385,461,556,
%T A239263 663,956,1137,1353,1603,2222,2625,3093,3622,4956,5796,6790,7907,10578,
%U A239263 12299,14283,16558,21830,25269,29175,33607,43656,50227,57723,66199,85183
%N A239263 Number of partitions of n having (sum of odd parts) >= (sum of even parts).
%H A239263 Alois P. Heinz, <a href="/A239263/b239263.txt">Table of n, a(n) for n = 0..500</a>
%F A239263 a(n) + A239259(n) = A000041(n).
%e A239263 a(8) counts these 14 partitions:  71, 53, 521, 5111, 431, 41111, 332, 3311, 3221, 32111, 311111, 221111, 2111111, 11111111.
%t A239263 z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
%t A239263 t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
%t A239263 t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
%t A239263 t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
%t A239263 t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
%t A239263 t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
%t A239263 (* _Peter J. C. Moses_, Mar 12 2014 *)
%Y A239263 Cf. A239259, A239260, A239261, A239262, A000041.
%K A239263 nonn,easy
%O A239263 0,4
%A A239263 _Clark Kimberling_, Mar 13 2014