A237258 Number of strict partitions of 2n that include a partition of n.

1, 0, 0, 1, 1, 3, 4, 7, 9, 16, 21, 32, 43, 63, 84, 122, 158, 220, 293, 393, 511, 685, 881, 1156, 1485, 1925, 2445, 3147, 3952, 5019, 6323, 7924, 9862, 12336, 15259, 18900, 23294, 28646, 35091, 42985, 52341, 63694, 77336, 93588, 112973, 136367, 163874, 196638

Offset

0,6

Comments

A strict partition is a partition into distinct parts.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..200

Formula

a(n) = A237194(2n,n).

Example

a(5) counts these partitions of 10: [5,4,1], [5,3,2], [4,3,2,1].

Mathematica

z = 24; Table[theTotals = Map[{#, Map[Total, Subsets[#]]} &,  Select[IntegerPartitions[2 nn], # == DeleteDuplicates[#] &]]; Length[Map[#[[1]] &, Select[theTotals, Length[Position[#[[2]], nn]] >= 1 &]]], {nn, z}] (* Peter J. C. Moses, Feb 04 2014 *)

Crossrefs

Cf. A000009, A237194, A235130.

The non-strict version is A002219, ranked by A357976.

These partitions are ranked by A357854.

A000712 counts distinct submultisets of partitions, strict A032302.

A304792 counts subset-sums of partitions, positive A276024, strict A284640.

Cf. A006827, A064914, A108917, A276107, A300061, A357879.

Sequence in context: A169898 A281734 A086336 * A108796 A364684 A048849

Adjacent sequences: A237255 A237256 A237257 * A237259 A237260 A237261

Keyword

nonn

Author

Clark Kimberling, Feb 05 2014

Extensions

a(31)-a(47) from Alois P. Heinz, Feb 07 2014

Status

approved