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%I #14 Jun 04 2017 05:55:11
%S 1,6,16,36,92,236,622,1658,4468,12132,33146,90998,250802,693426,
%T 1922118,5339006,14854932,41387764,115438672,322267784,900314242,
%U 2516648618,7038066876,19690060024,55102545322,154241612986
%N Number of base 6 circular n-digit numbers with adjacent digits differing by 1 or less.
%C [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C a(n) = T(n, 6) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,6}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%F Conjectures from _Colin Barker_, Jun 04 2017: (Start)
%F G.f.: (1 - 10*x^2 + 27*x^4 - 8*x^5 - 5*x^6) / ((1 - 2*x - x^2 + x^3)*(1 - 4*x + 3*x^2 + x^3)).
%F a(n) = 6*a(n-1) - 10*a(n-2) + 9*a(n-4) - 2*a(n-5) - a(n-6) for n>6.
%F (End)
%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>1)+($[(i+1)mod N]`-$[i]`>1))
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 28 2006
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