A237365 Number of partitions of n for which 2*(number of distinct parts) > (number of parts).

0, 1, 1, 2, 3, 5, 5, 9, 12, 17, 22, 30, 38, 51, 64, 89, 110, 141, 177, 225, 279, 352, 436, 543, 669, 827, 1012, 1244, 1494, 1827, 2214, 2674, 3219, 3877, 4646, 5571, 6645, 7914, 9412, 11181, 13226, 15641, 18466, 21739, 25563, 30103, 35250, 41275, 48281, 56353

Offset

0,4

Comments

A237363(n) + a(n) = A000041(n).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

Example

Among the 22 partitions of 8, these qualify:  [8], [7,1], [6,2], [6,1,1], [5,3], [5,2,1], [4,3,1], [4,2,2], [4,2,1,1], [3,3,2], [3,2,2,1], [3,2,1,1,1], and the remaining 10 do not, so that a(8) = 12.

Mathematica

z = 50; t = Map[Length[Select[IntegerPartitions[#], 2*Length[DeleteDuplicates[#]] <= Length[#] &]] &, Range[z]] (*A237363*)
Table[PartitionsP[n] - t[[n]], {n, 1, z}] (*A237365*) (* Peter J. C. Moses, Feb 06 2014 *)

Crossrefs

Cf. A237363.

Sequence in context: A183562 A222705 A241381 * A322770 A257008 A338750

Adjacent sequences: A237362 A237363 A237364 * A237366 A237367 A237368

Keyword

nonn

Author

Clark Kimberling, Feb 06 2014

Status

approved