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

Author

Clark Kimberling, Feb 06 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A237363.

Programs

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 *)