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A215333 Smooth necklaces with 7 colors.

%I A215333 #8 Jun 17 2019 05:52:10
%S A215333 1,7,13,24,55,126,330,836,2232,5926,15932,42849,116011,314375,854952,
%T A215333 2329162,6359574,17393334,47653952,130752976,359275056,988458426,
%U A215333 2722803495
%N A215333 Smooth necklaces with 7 colors.
%C A215333 We call a necklace (x[1],x[2],...,x[n]) smooth if abs(x[k]-x[k-1]) <= 1 for 2<=k<=n.
%e A215333 The smooth pre-necklaces, necklaces (N), and Lyndon words (L) of length 3 with 4 colors (using symbols ".", "1", "2", "3", "4", "5", and "6") are:
%e A215333     ...   1      .  N
%e A215333     ..1   3    ..1  N L
%e A215333     .1.   2     1.
%e A215333     .11   3    .11  N L
%e A215333     .12   3    .12  N L
%e A215333     111   1      1  N
%e A215333     112   3    112  N L
%e A215333     121   2     21
%e A215333     122   3    122  N L
%e A215333     123   3    123  N L
%e A215333     222   1      2  N
%e A215333     223   3    223  N L
%e A215333     232   2     32
%e A215333     233   3    233  N L
%e A215333     234   3    234  N L
%e A215333     333   1      3  N
%e A215333     334   3    334  N L
%e A215333     343   2     43
%e A215333     344   3    344  N L
%e A215333     345   3    345  N L
%e A215333     444   1      4  N
%e A215333     445   3    445  N L
%e A215333     454   2     54
%e A215333     455   3    455  N L
%e A215333     456   3    456  N L
%e A215333     555   1      5  N
%e A215333     556   3    556  N L
%e A215333     565   2     65
%e A215333     566   3    566  N L
%e A215333     666   1      6  N
%e A215333 There are 30 pre-necklaces, 24 necklaces, and 17 Lyndon words.
%e A215333 So a(3) = 24.
%Y A215333 Cf. A215327 (smooth necklaces with 3 colors).
%K A215333 nonn,more
%O A215333 0,2
%A A215333 _Joerg Arndt_, Aug 08 2012
%E A215333 More terms from _Joerg Arndt_, Jun 17 2019