A241651 Number of partitions p of n such that 2*(number of even numbers in p) < (number of odd numbers in p).

0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 16, 22, 27, 38, 47, 66, 81, 112, 136, 187, 227, 301, 363, 473, 568, 727, 862, 1088, 1289, 1596, 1876, 2304, 2697, 3265, 3810, 4583, 5327, 6358, 7354, 8736, 10101, 11924, 13750, 16195, 18653, 21883, 25177, 29484, 33906

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = A241652(n) - A241653(n) for n >= 0.

a(n) + A241653(n) + A241655(n) = A000041(n) for n >= 0.

Example

a(6) counts these 4 partitions:  51, 33, 3111, 111111.

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_ /; 2 s0[p] < s1[p]], {n, 0, z}]  (* A241651 *)
Table[Count[f[n], p_ /; 2 s0[p] <= s1[p]], {n, 0, z}] (* A241652 *)
Table[Count[f[n], p_ /; 2 s0[p] == s1[p]], {n, 0, z}] (* A241653 *)
Table[Count[f[n], p_ /; 2 s0[p] >= s1[p]], {n, 0, z}] (* A241654 *)
Table[Count[f[n], p_ /; 2 s0[p] > s1[p]], {n, 0, z}]  (* A241655 *)

Crossrefs

Cf. A241652, A241653, A241654, A241655.

Sequence in context: A238708 A266751 A063827 * A127217 A240735 A057042

Adjacent sequences: A241648 A241649 A241650 * A241652 A241653 A241654

Keyword

nonn,easy

Author

Clark Kimberling, Apr 27 2014

Status

approved