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

1, 1, 1, 2, 3, 5, 6, 8, 14, 19, 24, 30, 49, 61, 75, 93, 144, 177, 217, 260, 385, 461, 556, 663, 956, 1137, 1353, 1603, 2222, 2625, 3093, 3622, 4956, 5796, 6790, 7907, 10578, 12299, 14283, 16558, 21830, 25269, 29175, 33607, 43656, 50227, 57723, 66199, 85183

Offset

0,4

Links

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

Formula

a(n) + A239259(n) = A000041(n).

Example

a(8) counts these 14 partitions:  71, 53, 521, 5111, 431, 41111, 332, 3311, 3221, 32111, 311111, 221111, 2111111, 11111111.

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, A239260, A239261, A239262, A000041.

Sequence in context: A239135 A179791 A139443 * A216293 A088497 A088485

Adjacent sequences: A239260 A239261 A239262 * A239264 A239265 A239266

Keyword

nonn,easy

Author

Clark Kimberling, Mar 13 2014

Status

approved