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 A371794 #6 Apr 08 2024 09:13:58
%S A371794 0,1,1,2,2,3,3,5,5,8,7,12,11,18,15,27,23,38,30,54,43,76,57,104,79,142,
%T A371794 102,192,138,256,174,340,232,448,292,585,375,760,471,982,602,1260,741,
%U A371794 1610,935,2048,1148,2590,1425,3264,1733,4097,2137,5120,2571,6378
%N A371794 Number of non-biquanimous strict integer partitions of n.
%C A371794 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 A371794 The a(1) = 1 through a(11) = 12 strict partitions:
%e A371794 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e A371794 (21) (31) (32) (42) (43) (53) (54) (64) (65)
%e A371794 (41) (51) (52) (62) (63) (73) (74)
%e A371794 (61) (71) (72) (82) (83)
%e A371794 (421) (521) (81) (91) (92)
%e A371794 (432) (631) (A1)
%e A371794 (531) (721) (542)
%e A371794 (621) (632)
%e A371794 (641)
%e A371794 (731)
%e A371794 (821)
%e A371794 (5321)
%t A371794 biqQ[y_]:=MemberQ[Total/@Subsets[y],Total[y]/2];
%t A371794 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!biqQ[#]&]],{n,0,30}]
%Y A371794 The complement is counted by A237258 aerated, ranks A357854.
%Y A371794 Even bisection is A321142, odd A078408.
%Y A371794 This is the "bi-" version of A371736, complement A371737.
%Y A371794 A002219 aerated counts biquanimous partitions, ranks A357976.
%Y A371794 A006827 and A371795 count non-biquanimous partitions, ranks A371731.
%Y A371794 A108917 counts knapsack partitions, ranks A299702, strict A275972.
%Y A371794 A321451 counts non-quanimous partitions, ranks A321453.
%Y A371794 A321452 counts quanimous partitions, ranks A321454.
%Y A371794 A366754 counts non-knapsack partitions, ranks A299729, strict A316402.
%Y A371794 A371781 lists numbers with biquanimous prime signature, complement A371782.
%Y A371794 A371783 counts k-quanimous partitions.
%Y A371794 A371789 counts non-quanimous sets, differences A371790.
%Y A371794 A371791 counts biquanimous sets, differences A232466.
%Y A371794 A371792 counts non-biquanimous sets, differences A371793.
%Y A371794 A371796 counts quanimous sets, differences A371797.
%Y A371794 Cf. A064914, A279787, A305551, A318434, A365543, A365663, A365661, A366320, A365925, A367094, A371788.
%K A371794 nonn
%O A371794 0,4
%A A371794 _Gus Wiseman_, Apr 07 2024