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A237365 Number of partitions of n for which 2*(number of distinct parts) > (number of parts). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A265822

Adjacent sequences:  A237362 A237363 A237364 * A237366 A237367 A237368

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 06 2014

STATUS

approved

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Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)