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 A325549 #6 May 11 2019 18:31:41
%S A325549 1,1,2,3,5,4,10,16,23,34,53,66,113,164,262,380,567,821,1217,1778,2702,
%T A325549 3919,5760,8520,12375
%N A325549 Number of necklace compositions of n with distinct circular differences.
%C A325549 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.
%C A325549 The circular differences of a composition c of length k are c_{i + 1} - c_i for i < k and c_1 - c_i for i = k. For example, the circular differences of (1,2,1,3) are (1,-1,2,-2).
%H A325549 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325549 The a(1) = 1 through a(8) = 16 necklace compositions:
%e A325549 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325549 (12) (13) (14) (15) (16) (17)
%e A325549 (112) (23) (24) (25) (26)
%e A325549 (113) (114) (34) (35)
%e A325549 (122) (115) (116)
%e A325549 (124) (125)
%e A325549 (133) (134)
%e A325549 (142) (143)
%e A325549 (223) (152)
%e A325549 (1213) (224)
%e A325549 (233)
%e A325549 (1124)
%e A325549 (1142)
%e A325549 (1214)
%e A325549 (11213)
%e A325549 (11312)
%t A325549 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325549 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],neckQ[#]&&UnsameQ@@Append[Differences[#],First[#]-Last[#]]&]],{n,15}]
%Y A325549 Cf. A000079, A000740, A008965, A034297, A059966, A070211, A318728, A318748, A320348, A325545, A325551, A325554, A325556.
%K A325549 nonn,more
%O A325549 1,3
%A A325549 _Gus Wiseman_, May 10 2019