A237269 Number of partitions of n such that at least half the parts are identical.

1, 1, 2, 3, 5, 7, 10, 14, 20, 26, 35, 47, 61, 79, 102, 129, 165, 208, 260, 325, 404, 498, 616, 756, 925, 1126, 1374, 1662, 2013, 2427, 2922, 3506, 4206, 5021, 5998, 7132, 8485, 10057, 11922, 14081, 16627, 19583, 23053, 27065, 31768, 37189, 43527, 50826, 59322

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Example

Of the 15 partitions of 7, only [1,2,4] does not qualify, so that a(7) = 14.

Mathematica

Map[Length[Select[Map[Max[Map[Last, Tally[#]]]/Length[#] &, IntegerPartitions[#]], # >= 1/2 &]] &, Range[50]]  (* Peter J. C. Moses, Feb 05 2014 *)

Crossrefs

Cf. A000041.

Sequence in context: A054405 A155167 A325858 * A116634 A035960 A288254

Adjacent sequences: A237266 A237267 A237268 * A237270 A237271 A237272

Keyword

nonn

Author

Clark Kimberling, Feb 05 2014

Status

approved