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%I #10 Apr 21 2024 10:00:39
%S 1,1,5,23,105,449,1902,7828,31976,129200,520425,2088217,8371186,
%T 33514797,134140430,536699674,2147154667,8589198795,34358341823,
%U 137435830265,549749857574,2199010044813,8796067657649,35184315676573,140737380485376,562949713881526
%N Number of ordered biquanimous partitions of 2n.
%C 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.
%e From _Gus Wiseman_, Apr 19 2024: (Start)
%e The a(0) = 1 through a(3) = 23 biquanimous compositions:
%e () (11) (22) (33)
%e (112) (123)
%e (121) (132)
%e (211) (213)
%e (1111) (231)
%e (312)
%e (321)
%e (1113)
%e (1122)
%e (1131)
%e (1212)
%e (1221)
%e (1311)
%e (2112)
%e (2121)
%e (2211)
%e (3111)
%e (11112)
%e (11121)
%e (11211)
%e (12111)
%e (21111)
%e (111111)
%e (End)
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[2n], MemberQ[Total/@Subsets[#],n]&]],{n,0,5}] (* _Gus Wiseman_, Apr 19 2024 *)
%Y The unordered version (integer partitions) is A002219, ranks A357976.
%Y The unordered complement is A371795, even case A006827, ranks A371731.
%Y The complement is counted by A371956.
%Y These compositions have ranks A372120, complement A372119.
%Y A237258 (aerated) counts biquanimous strict partitions, ranks A357854.
%Y A321142 and A371794 count non-biquanimous strict partitions.
%Y A371791 counts biquanimous sets, differences A232466.
%Y A371792 counts non-biquanimous sets, differences A371793.
%Y Cf. A027187, A035470, A357879, A367094, A371781, A371782, A371783.
%K nonn,changed
%O 0,3
%A _Christian G. Bower_, Oct 12 2001
%E More terms from _Alois P. Heinz_, Jun 12 2017
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