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

0,4

Links

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

Formula

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

Example

a(8) counts these 10 partitions:  71, 53, 521, 5111, 332, 3311, 32111, 311111, 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, A239263, A000041.

Sequence in context: A034803 A205885 A360690 * A288496 A292726 A258621

Adjacent sequences: A239259 A239260 A239261 * A239263 A239264 A239265

Keyword

nonn,easy

Author

Clark Kimberling, Mar 13 2014

Status

approved