A064914 - OEIS

A064914

Number of ordered biquanimous partitions of 2n.

1, 1, 5, 23, 105, 449, 1902, 7828, 31976, 129200, 520425, 2088217, 8371186, 33514797, 134140430, 536699674, 2147154667, 8589198795, 34358341823, 137435830265, 549749857574, 2199010044813, 8796067657649, 35184315676573, 140737380485376, 562949713881526

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OFFSET

0,3

COMMENTS

A biquanimous partition is one that can be bisected into two equal sized parts: e.g. 3+2+1 is a biquanimous partition of 6 as it contains 3 and 2+1, but 5+1 is not.

LINKS

Table of n, a(n) for n=0..25.

EXAMPLE

From Gus Wiseman, Apr 19 2024: (Start)

The a(0) = 1 through a(3) = 23 biquanimous compositions:

() (11) (22) (33)

(112) (123)

(121) (132)

(211) (213)

(1111) (231)

(312)

(321)

(1113)

(1122)

(1131)

(1212)

(1221)

(1311)

(2112)

(2121)

(2211)

(3111)

(11112)

(11121)

(11211)

(12111)

(21111)

(111111)

(End)

MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[2n], MemberQ[Total/@Subsets[#], n]&]], {n, 0, 5}] (* Gus Wiseman, Apr 19 2024 *)

CROSSREFS

The unordered version (integer partitions) is A002219, ranks A357976.

The unordered complement is A371795, even case A006827, ranks A371731.

The complement is counted by A371956.

These compositions have ranks A372120, complement A372119.

A237258 (aerated) counts biquanimous strict partitions, ranks A357854.

A321142 and A371794 count non-biquanimous strict partitions.

A371791 counts biquanimous sets, differences A232466.

A371792 counts non-biquanimous sets, differences A371793.

Cf. A027187, A035470, A357879, A367094, A371781, A371782, A371783.

Sequence in context: A167660 A290924 A026760 * A243873 A239406 A107839

Adjacent sequences: A064911 A064912 A064913 * A064915 A064916 A064917

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 12 2001

EXTENSIONS

More terms from Alois P. Heinz, Jun 12 2017

STATUS

approved