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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). 38
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
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
Sequence in context: A200089 A330686 A117956 * A360689 A110662 A265289
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 27 2014
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)