A239259 Number of partitions of n having (sum of odd parts) < (sum of even parts).

0, 0, 1, 1, 2, 2, 5, 7, 8, 11, 18, 26, 28, 40, 60, 83, 87, 120, 168, 230, 242, 331, 446, 592, 619, 821, 1083, 1407, 1496, 1940, 2511, 3220, 3393, 4347, 5520, 6976, 7399, 9338, 11732, 14627, 15508, 19314, 23999, 29654, 31519, 38907, 47835, 58555, 62090, 75942

Offset: 0

Author

Clark Kimberling, Mar 13 2014

Keywords

• nonn
• easy

Examples

			a(8) counts these 8 partitions:  8, 62, 611, 44, 422, 4211, 2222, 22211.
		

Links

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

Crossrefs

Cf. A239260, A239261, A239262, 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) + A239263(n) = A000041(n).