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A241643 Number of partitions p of n such that (number of even numbers in p) = 2*(number of odd numbers in p). 5
1, 0, 0, 0, 0, 0, 0, 1, 1, 4, 3, 11, 9, 22, 16, 40, 31, 65, 47, 98, 74, 140, 103, 196, 146, 261, 194, 339, 265, 447, 352, 577, 486, 747, 674, 1001, 960, 1351, 1401, 1853, 2065, 2611, 3048, 3700, 4514, 5268, 6636, 7537, 9647, 10714, 13901, 15103, 19734, 21173 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

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

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) = A241642(n) - A241641(n) for n >= 0.

a(n) + A241641(n) + A241645(n) = A000041(n) for n >= 0.

EXAMPLE

a(9) counts these 4 partitions:  621, 432, 4221, 42111.

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] < 2 s1[p]], {n, 0, z}]  (* A241641 *)

Table[Count[f[n], p_ /; s0[p] <= 2 s1[p]], {n, 0, z}] (* A241642 *)

Table[Count[f[n], p_ /; s0[p] == 2 s1[p]], {n, 0, z}] (* A241643 *)

Table[Count[f[n], p_ /; s0[p] >= 2 s1[p]], {n, 0, z}] (* A241644 *)

Table[Count[f[n], p_ /; s0[p] > 2 s1[p]], {n, 0, z}]  (* A241645 *)

CROSSREFS

Cf. A241641, A241642, A241644, A241645.

Sequence in context: A353341 A346614 A005013 * A086564 A316966 A295727

Adjacent sequences:  A241640 A241641 A241642 * A241644 A241645 A241646

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified May 22 08:21 EDT 2022. Contains 353933 sequences. (Running on oeis4.)