This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371956 #5 Apr 20 2024 10:51:38
%S A371956 0,1,3,9,23,63,146,364
%N A371956 Number of non-biquanimous compositions of 2n.
%C A371956 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.
%e A371956 The a(1) = 1 through a(3) = 9 compositions:
%e A371956 (2) (4) (6)
%e A371956 (1,3) (1,5)
%e A371956 (3,1) (2,4)
%e A371956 (4,2)
%e A371956 (5,1)
%e A371956 (1,1,4)
%e A371956 (1,4,1)
%e A371956 (2,2,2)
%e A371956 (4,1,1)
%t A371956 Table[Length[Select[Join@@Permutations/@IntegerPartitions[2n], !MemberQ[Total/@Subsets[#],n]&]],{n,0,5}]
%Y A371956 The unordered complement is A002219, ranks A357976.
%Y A371956 The unordered version is A006827, even case of A371795, ranks A371731.
%Y A371956 The complement is counted by A064914.
%Y A371956 These compositions have ranks A372119, complement A372120.
%Y A371956 A237258 (aerated) counts biquanimous strict partitions, ranks A357854.
%Y A371956 A321142 and A371794 count non-biquanimous strict partitions.
%Y A371956 A371791 counts biquanimous sets, differences A232466.
%Y A371956 A371792 counts non-biquanimous sets, differences A371793.
%Y A371956 Cf. A027187, A035470, A357879, A367094, A371781, A371782, A371783.
%K A371956 nonn,more
%O A371956 0,3
%A A371956 _Gus Wiseman_, Apr 20 2024