A241644 Number of partitions p of n such that (number of even numbers in p) >= 2*(number of odd numbers in p).

1, 0, 1, 0, 2, 0, 3, 1, 6, 4, 10, 11, 20, 23, 32, 44, 56, 76, 86, 124, 136, 193, 199, 293, 297, 430, 422, 619, 609, 884, 855, 1246, 1217, 1742, 1708, 2438, 2423, 3393, 3415, 4717, 4845, 6558, 6828, 9097, 9653, 12585, 13549, 17379, 18987, 23897, 26420, 32712

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..51.

Formula

a(n) = A241643(n) + A241645(n) for n >= 0.

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

Example

a(6) counts these 3 partitions:  6, 42, 222.

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, A241643, A241645.

Sequence in context: A340385 A143351 A350962 * A241640 A158449 A106533

Adjacent sequences: A241641 A241642 A241643 * A241645 A241646 A241647

Keyword

nonn,easy

Author

Clark Kimberling, Apr 27 2014

Status

approved