A241645 Number of partitions p of n such that (number of even numbers in p) > 2*(number of odd numbers in p).

0, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 1, 16, 4, 25, 11, 39, 26, 62, 53, 96, 97, 151, 169, 228, 280, 344, 437, 503, 669, 731, 995, 1034, 1437, 1463, 2042, 2014, 2864, 2780, 3947, 3780, 5397, 5139, 7317, 6913, 9842, 9340, 13183, 12519, 17609, 16859, 23416

Offset

0,5

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) = A241644(n) - A241643(n) for n >= 0.

a(n) + A241641(n) + A241643(n) = A000041(n) for n >= 0.

Example

a(8) counts these 5 partitions:  8, 62, 44, 422, 2222.

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, A241644.

Sequence in context: A240145 A240146 A035363 * A266774 A079977 A227093

Adjacent sequences: A241642 A241643 A241644 * A241646 A241647 A241648

Keyword

nonn,easy

Author

Clark Kimberling, Apr 27 2014

Status

approved