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 A325555 #4 May 12 2019 08:21:16
%S A325555 1,2,2,4,5,6,10,15,19,24,39,49,78,106,155,207,313,430,608,867,1239,
%T A325555 1670,2313,3220,4483
%N A325555 Number of necklace compositions of n with distinct differences up to sign.
%C A325555 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 A325555 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1).
%H A325555 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325555 The a(1) = 1 through a(8) = 15 necklace compositions:
%e A325555 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325555 (11) (12) (13) (14) (15) (16) (17)
%e A325555 (22) (23) (24) (25) (26)
%e A325555 (112) (113) (33) (34) (35)
%e A325555 (122) (114) (115) (44)
%e A325555 (132) (124) (116)
%e A325555 (133) (125)
%e A325555 (142) (134)
%e A325555 (223) (143)
%e A325555 (1132) (152)
%e A325555 (224)
%e A325555 (233)
%e A325555 (1124)
%e A325555 (1142)
%e A325555 (1322)
%t A325555 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325555 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Abs[Differences[#]]&&neckQ[#]&]],{n,15}]
%Y A325555 Cf. A000079, A008965, A235998, A242882, A325325, A325352, A325404, A325468, A325552, A325554, A325556.
%K A325555 nonn,more
%O A325555 1,2
%A A325555 _Gus Wiseman_, May 11 2019