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A241638 Number of partitions p of n such that (number of even numbers in p) = (number of odd numbers in p). 9
1, 0, 0, 1, 1, 4, 3, 8, 6, 13, 11, 20, 17, 31, 34, 47, 56, 78, 103, 125, 167, 203, 281, 315, 433, 487, 673, 745, 989, 1101, 1472, 1623, 2116, 2386, 3052, 3430, 4347, 4948, 6168, 7104, 8673, 10068, 12210, 14234, 17047, 20007, 23671, 27869, 32739, 38609, 45010 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Each number in p is counted once, regardless of its multiplicity.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A241637(n) - A241636(n) = A241639(n) - A241640(n) for n >= 0.

a(n) + A241636(n) + A241640(n) = A000041(n) for n >= 0.

a(n) = A242618(n,0). - Alois P. Heinz, May 19 2014

EXAMPLE

a(6) counts these 3 partitions:  411, 2211, 21111.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2],   0];

s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];

Table[Count[f[n], p_ /; s0[p] < s1[p]], {n, 0, z}]  (* A241636 *)

Table[Count[f[n], p_ /; s0[p] <= s1[p]], {n, 0, z}] (* A241637 *)

Table[Count[f[n], p_ /; s0[p] == s1[p]], {n, 0, z}] (* A241638 *)

Table[Count[f[n], p_ /; s0[p] >= s1[p]], {n, 0, z}] (* A241639 *)

Table[Count[f[n], p_ /; s0[p] > s1[p]], {n, 0, z}]  (* A241640 *)

CROSSREFS

Cf. A241636, A241637, A241639, A241640.

Sequence in context: A011451 A200089 A117956 * A110662 A265289 A302258

Adjacent sequences:  A241635 A241636 A241637 * A241639 A241640 A241641

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified October 14 17:27 EDT 2019. Contains 328022 sequences. (Running on oeis4.)