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

1, 0, 1, 1, 3, 2, 5, 7, 12, 11, 18, 26, 40, 40, 60, 83, 117, 120, 168, 230, 312, 331, 446, 592, 784, 821, 1083, 1407, 1826, 1940, 2511, 3220, 4097, 4347, 5520, 6976, 8779, 9338, 11732, 14627, 18196, 19314, 23999, 29654, 36503, 38907, 47835, 58555, 71484, 75942

Offset

0,5

Links

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

Formula

a(n) + A239262(n) = A000041(n).

Example

a(8) counts these 12 partitions:  8, 62, 611, 44, 431, 422, 4211, 41111, 3221, 2222, 22211, 221111.

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 *)

Crossrefs

Cf. A239259, A239261, A239262, A239263, A000041.

Sequence in context: A371221 A171018 A350192 * A013655 A223701 A220519

Adjacent sequences: A239257 A239258 A239259 * A239261 A239262 A239263

Keyword

nonn,easy

Author

Clark Kimberling, Mar 13 2014

Status

approved