A241643 Number of partitions p of n such that (number of even numbers in p) = 2*(number of odd numbers in p).

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

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