cp's OEIS Frontend

A239262 Number of partitions of n having (sum of odd parts) > (sum of even parts).

%I A239262 #7 Mar 15 2014 17:15:02
%S A239262 0,1,1,2,2,5,6,8,10,19,24,30,37,61,75,93,114,177,217,260,315,461,556,
%T A239262 663,791,1137,1353,1603,1892,2625,3093,3622,4252,5796,6790,7907,9198,
%U A239262 12299,14283,16558,19142,25269,29175,33607,38672,50227,57723,66199,75789
%N A239262 Number of partitions of n having (sum of odd parts) > (sum of even parts).
%H A239262 Alois P. Heinz, <a href="/A239262/b239262.txt">Table of n, a(n) for n = 0..500</a>
%F A239262 a(n) + A239260(n) = A000041(n).
%e A239262 a(8) counts these 10 partitions:  71, 53, 521, 5111, 332, 3311, 32111, 311111, 2111111, 11111111.
%t A239262 z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
%t A239262 t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
%t A239262 t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
%t A239262 t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
%t A239262 t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
%t A239262 t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
%t A239262 (* _Peter J. C. Moses_, Mar 12 2014 *)
%Y A239262 Cf. A239259, A239260, A239261, A239263, A000041.
%K A239262 nonn,easy
%O A239262 0,4
%A A239262 _Clark Kimberling_, Mar 13 2014