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.
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 complement is counted by A371956.
KEYWORD
nonn
AUTHOR
Christian G. Bower, Oct 12 2001
EXTENSIONS
More terms from Alois P. Heinz, Jun 12 2017
STATUS
approved