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

0, 1, 1, 2, 2, 5, 6, 8, 10, 19, 24, 30, 37, 61, 75, 93, 114, 177, 217, 260, 315, 461, 556, 663, 791, 1137, 1353, 1603, 1892, 2625, 3093, 3622, 4252, 5796, 6790, 7907, 9198, 12299, 14283, 16558, 19142, 25269, 29175, 33607, 38672, 50227, 57723, 66199, 75789

Offset: 0

Author

Clark Kimberling, Mar 13 2014

Keywords

• nonn
• easy

Examples

			a(8) counts these 10 partitions:  71, 53, 521, 5111, 332, 3311, 32111, 311111, 2111111, 11111111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A239259, A239260, A239261, A239263, A000041.

Programs

Mathematica

z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
(* Peter J. C. Moses, Mar 12 2014 *)

Formula

a(n) + A239260(n) = A000041(n).