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 A325786 #6 May 22 2019 21:00:16
%S A325786 1,1,2,2,4,7,12,19,41,71,141,255,509,924,1882,3395,6838,12715,25233,
%T A325786 47049
%N A325786 Number of complete necklace compositions of n.
%C A325786 A necklace composition of n is a finite sequence of positive integers summing to n that is lexicographically minimal among all of its cyclic rotations. A circular subsequence is a sequence of consecutive terms where the first and last parts are also considered consecutive. A necklace composition of n is complete if every positive integer from 1 to n is the sum of some circular subsequence.
%e A325786 The a(1) = 1 through a(8) = 19 necklace compositions:
%e A325786 (1) (11) (12) (112) (113) (123) (124) (1124)
%e A325786 (111) (1111) (122) (132) (142) (1133)
%e A325786 (1112) (1113) (1114) (1142)
%e A325786 (11111) (1122) (1123) (1214)
%e A325786 (1212) (1132) (1223)
%e A325786 (11112) (1213) (1322)
%e A325786 (111111) (1222) (11114)
%e A325786 (11113) (11123)
%e A325786 (11122) (11132)
%e A325786 (11212) (11213)
%e A325786 (111112) (11222)
%e A325786 (1111111) (11312)
%e A325786 (12122)
%e A325786 (111113)
%e A325786 (111122)
%e A325786 (111212)
%e A325786 (112112)
%e A325786 (1111112)
%e A325786 (11111111)
%t A325786 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325786 subalt[q_]:=Union[ReplaceList[q,{___,s__,___}:>{s}],DeleteCases[ReplaceList[q,{t___,__,u___}:>{u,t}],{}]];
%t A325786 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],neckQ[#]&&Union[Total/@subalt[#]]==Range[n]&]],{n,15}]
%Y A325786 Cf. A000740, A002033, A008965, A103295, A108917, A126796, A276024, A325549, A325682, A325781, A325788, A325789, A325791.
%K A325786 nonn,more
%O A325786 1,3
%A A325786 _Gus Wiseman_, May 22 2019