A371956 Number of non-biquanimous compositions of 2n.

0, 1, 3, 9, 23, 63, 146, 364

Offset: 0

Author

Gus Wiseman, Apr 20 2024

Keywords

• nonn
• more

Comments

A finite multiset of numbers is defined to be biquanimous iff it can be partitioned into two multisets with equal sums. Biquanimous partitions are counted by A002219 and ranked by A357976.

Examples

			The a(1) = 1 through a(3) = 9 compositions:
  (2)  (4)    (6)
       (1,3)  (1,5)
       (3,1)  (2,4)
              (4,2)
              (5,1)
              (1,1,4)
              (1,4,1)
              (2,2,2)
              (4,1,1)
		

Crossrefs

The unordered complement is A002219, ranks A357976.

The unordered version is A006827, even case of A371795, ranks A371731.

The complement is counted by A064914.

These compositions have ranks A372119, complement A372120.

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.

Programs

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[2n], !MemberQ[Total/@Subsets[#],n]&]],{n,0,5}]