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 A325789 #11 Jun 07 2019 16:32:47
%S A325789 1,1,2,1,1,1,3,1,1,1,1,1,5,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,11,1,1,1,
%T A325789 1,1,1,1,1,1
%N A325789 Number of perfect necklace compositions of n.
%C A325789 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 last and first parts are also considered consecutive. A necklace composition of n is perfect if every positive integer from 1 to n is the sum of exactly one distinct circular subsequence.
%F A325789 For n > 1, a(n) = A325787(n) + 1.
%e A325789 The a(1) = 1 , a(2) = 1, a(3) = 2, a(7) = 3, a(13) = 5, and a(31) = 11 perfect necklace compositions (A = 10, B = 11, C = 12, D = 13, E = 14):
%e A325789 1 11 12 124 1264 12546D
%e A325789 111 142 1327 1274C5
%e A325789 1111111 1462 13278A
%e A325789 1723 13625E
%e A325789 1111111111111 15C472
%e A325789 17324E
%e A325789 1A8723
%e A325789 1D6452
%e A325789 1E4237
%e A325789 1E5263
%e A325789 1111111111111111111111111111111
%t A325789 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325789 subalt[q_]:=Union[ReplaceList[q,{___,s__,___}:>{s}],DeleteCases[ReplaceList[q,{t___,__,u___}:>{u,t}],{}]];
%t A325789 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],neckQ[#]&&Sort[Total/@subalt[#]]==Range[n]&]],{n,10}]
%Y A325789 Cf. A002033, A008965, A103300, A108917, A126796, A325676, A325679, A325685, A325780, A325782, A325786, A325787, A325789.
%K A325789 nonn,more
%O A325789 1,3
%A A325789 _Gus Wiseman_, May 22 2019