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

Author

Clark Kimberling, Feb 05 2014

Keywords

• nonn

Comments

A strict partition is a partition into distinct parts.

Examples

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

Links

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

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.

Programs

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 *)

Formula

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

Extensions

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