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 A329145 #5 Nov 10 2019 20:28:44
%S A329145 0,0,1,3,9,19,45,93,197,405,837,1697,3465,7011,14193,28653,57825,
%T A329145 116471,234549,471801,948697,1906407,3829581,7689357,15435033,
%U A329145 30973005,62137797,124630149,249922665,501078345,1004468157,2013263853,4034666121,8084640465
%N A329145 Number of non-necklace compositions of n.
%C A329145 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.
%F A329145 a(n) = 2^(n-1) - A008965(n).
%e A329145 The a(3) = 1 through a(6) = 19 compositions:
%e A329145 (21) (31) (32) (42)
%e A329145 (121) (41) (51)
%e A329145 (211) (131) (141)
%e A329145 (212) (213)
%e A329145 (221) (231)
%e A329145 (311) (312)
%e A329145 (1121) (321)
%e A329145 (1211) (411)
%e A329145 (2111) (1131)
%e A329145 (1221)
%e A329145 (1311)
%e A329145 (2112)
%e A329145 (2121)
%e A329145 (2211)
%e A329145 (3111)
%e A329145 (11121)
%e A329145 (11211)
%e A329145 (12111)
%e A329145 (21111)
%t A329145 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A329145 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!neckQ[#]&]],{n,10}]
%Y A329145 Numbers whose prime signature is not a necklace are A329142.
%Y A329145 Binary necklaces are A000031.
%Y A329145 Necklace compositions are A008965.
%Y A329145 Lyndon compositions are A059966.
%Y A329145 Numbers whose reversed binary expansion is a necklace are A328595.
%Y A329145 Cf. A000740, A001037, A019536, A070211, A178472, A318731, A329138, A329141.
%K A329145 nonn
%O A329145 1,4
%A A329145 _Gus Wiseman_, Nov 10 2019