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 A371795 #10 Feb 13 2025 07:56:09
%S A371795 0,1,1,3,2,7,5,15,8,30,17,56,24,101,46,176,64,297,107,490,147,792,242,
%T A371795 1255,302,1958,488,3010,629,4565,922,6842,1172,10143,1745,14883,2108,
%U A371795 21637,3104,31185,3737,44583,5232,63261,6419,89134,8988,124754,10390,173525
%N A371795 Number of non-biquanimous integer partitions of n.
%C A371795 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 A371795 The a(1) = 1 through a(8) = 8 partitions:
%e A371795 (1) (2) (3) (4) (5) (6) (7) (8)
%e A371795 (21) (31) (32) (42) (43) (53)
%e A371795 (111) (41) (51) (52) (62)
%e A371795 (221) (222) (61) (71)
%e A371795 (311) (411) (322) (332)
%e A371795 (2111) (331) (521)
%e A371795 (11111) (421) (611)
%e A371795 (511) (5111)
%e A371795 (2221)
%e A371795 (3211)
%e A371795 (4111)
%e A371795 (22111)
%e A371795 (31111)
%e A371795 (211111)
%e A371795 (1111111)
%t A371795 biqQ[y_]:=MemberQ[Total/@Subsets[y],Total[y]/2];
%t A371795 Table[Length[Select[IntegerPartitions[n],Not@*biqQ]],{n,0,15}]
%o A371795 (PARI) a(n) = if(n%2, numbpart(n), my(v=partitions(n/2), w=List([])); for(i=1, #v, for(j=1, i, listput(w, vecsort(concat(v[i], v[j]))))); numbpart(n)-#Set(w)); \\ _Jinyuan Wang_, Feb 13 2025
%Y A371795 The complement is counted by A002219 aerated, ranks A357976.
%Y A371795 Even bisection is A006827, odd A058695.
%Y A371795 The strict complement is A237258, ranks A357854.
%Y A371795 This is the "bi-" version of A321451, ranks A321453.
%Y A371795 The complement is the "bi-" version of A321452, ranks A321454.
%Y A371795 These partitions have ranks A371731.
%Y A371795 The strict case is A371794, bisections A321142, A078408.
%Y A371795 A108917 counts knapsack partitions, ranks A299702, strict A275972.
%Y A371795 A366754 counts non-knapsack partitions, ranks A299729, strict A316402.
%Y A371795 A371736 counts non-quanimous strict partitons, complement A371737.
%Y A371795 A371781 lists numbers with biquanimous prime signature, complement A371782.
%Y A371795 A371783 counts k-quanimous partitions.
%Y A371795 A371789 counts non-quanimous sets, differences A371790.
%Y A371795 A371791 counts biquanimous sets, differences A232466.
%Y A371795 A371792 counts non-biquanimous sets, differences A371793.
%Y A371795 A371796 counts quanimous sets, differences A371797.
%Y A371795 Cf. A035470, A064914, A305551, A336137, A365543, A365661, A365663, A366320, A365925, A367094, A371788.
%K A371795 nonn
%O A371795 0,4
%A A371795 _Gus Wiseman_, Apr 07 2024
%E A371795 More terms from _Jinyuan Wang_, Feb 13 2025