A241642 Number of partitions p of n such that (number of even numbers in p) <= 2*(number of odd numbers in p).

1, 1, 1, 3, 3, 7, 8, 15, 17, 30, 35, 56, 66, 100, 119, 172, 206, 286, 346, 464, 565, 739, 906, 1158, 1424, 1789, 2208, 2730, 3374, 4128, 5101, 6173, 7618, 9148, 11276, 13446, 16514, 19595, 24001, 28321, 34558, 40636, 49394, 57864, 70036, 81817, 98645, 114912

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = A241641(n) + A241643(n) for n >= 0.

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

Example

a(6) counts these 8 partitions:  51, 411, 33, 321, 3111, 2211, 21111, 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_ /; 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, A241643, A241644, A241645.

Sequence in context: A218572 A218573 A117989 * A086543 A281616 A110618

Adjacent sequences: A241639 A241640 A241641 * A241643 A241644 A241645

Keyword

nonn,easy

Author

Clark Kimberling, Apr 27 2014

Status

approved