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A239259 Number of partitions of n having (sum of odd parts) < (sum of even parts). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) + A239263(n) = A000041(n).

EXAMPLE

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

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. A239260, A239261, A239262, A239263, A000041.

Sequence in context: A035586 A216392 A287908 * A188623 A256358 A241761

Adjacent sequences:  A239256 A239257 A239258 * A239260 A239261 A239262

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 13 2014

STATUS

approved

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Last modified May 23 11:05 EDT 2019. Contains 323513 sequences. (Running on oeis4.)