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A237363 Number of partitions of n for which 2*(number of distinct parts) <= (number of parts). 2
1, 0, 1, 1, 2, 2, 6, 6, 10, 13, 20, 26, 39, 50, 71, 87, 121, 156, 208, 265, 348, 440, 566, 712, 906, 1131, 1424, 1766, 2224, 2738, 3390, 4168, 5130, 6266, 7664, 9312, 11332, 13723, 16603, 20004, 24112, 28942, 34708, 41522, 49612, 59031, 70308, 83479, 98992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) + A237365(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:  [5,1,1,1], [4,4], [4,1,1,1,1], [3,3,1,1], [3,1,1,1,1,1], [2,2,2,2], [2,2,2,1,1], [2,2,1,1,1,1], [2,1,1,1,1,1,1], [1,1,1,1,1,1,1,1], and the remaining 12 do not, so that a(8) = 10.

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. A237365.

Sequence in context: A289835 A168276 A039722 * A082542 A162776 A032302

Adjacent sequences:  A237360 A237361 A237362 * A237364 A237365 A237366

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 06 2014

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)