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 A325556 #4 May 12 2019 08:21:23
%S A325556 1,1,1,1,1,1,3,7,9,13,25,27,51,63,95,123,179,205,305,409,559,715,1009,
%T A325556 1337,1869
%N A325556 Number of necklace compositions of n with distinct circular differences up to sign.
%C A325556 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 A325556 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 A325556 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325556 The a(1) = 1 through a(10) = 13 necklace compositions:
%e A325556 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
%e A325556 (124) (125) (126) (127)
%e A325556 (142) (134) (162) (136)
%e A325556 (143) (1125) (145)
%e A325556 (152) (1134) (154)
%e A325556 (1124) (1143) (163)
%e A325556 (1142) (1152) (172)
%e A325556 (1224) (235)
%e A325556 (1422) (253)
%e A325556 (1126)
%e A325556 (1162)
%e A325556 (1225)
%e A325556 (1522)
%t A325556 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325556 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Abs[Differences[Append[#,First[#]]]]&&neckQ[#]&]],{n,15}]
%Y A325556 Cf. A000079, A000740, A008965, A235998, A318728, A325324, A325325, A325349, A325549, A325553, A325555, A325588, A325590.
%K A325556 nonn,more
%O A325556 1,7
%A A325556 _Gus Wiseman_, May 11 2019