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 A325554 #5 May 12 2019 08:21:07
%S A325554 1,2,2,4,5,6,11,18,26,38,60,90,139,213,329,501,747,1144,1712,2548,
%T A325554 3836,5732,8442,12654,18624
%N A325554 Number of necklace compositions of n with distinct differences.
%C A325554 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 A325554 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 A325554 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325554 The a(1) = 1 through a(8) = 18 necklace compositions:
%e A325554 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325554 (11) (12) (13) (14) (15) (16) (17)
%e A325554 (22) (23) (24) (25) (26)
%e A325554 (112) (113) (33) (34) (35)
%e A325554 (122) (114) (115) (44)
%e A325554 (132) (124) (116)
%e A325554 (133) (125)
%e A325554 (142) (134)
%e A325554 (223) (143)
%e A325554 (1132) (152)
%e A325554 (1213) (224)
%e A325554 (233)
%e A325554 (1124)
%e A325554 (1142)
%e A325554 (1214)
%e A325554 (1322)
%e A325554 (11213)
%e A325554 (11312)
%t A325554 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A325554 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Differences[#]&&neckQ[#]&]],{n,15}]
%Y A325554 Cf. A000079, A008965, A235998, A242882, A318728, A325325, A325404, A325468, A325545, A325549, A325550, A325555.
%K A325554 nonn,more
%O A325554 1,2
%A A325554 _Gus Wiseman_, May 11 2019