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A239263 Number of partitions of n having (sum of odd parts) >= (sum of even parts). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 16:25 EDT 2021. Contains 346447 sequences. (Running on oeis4.)