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%I #14 Jun 03 2017 12:59:07
%S 1,8,22,50,130,338,904,2444,6682,18410,51052,142304,398380,1119308,
%T 3154558,8914010,25246282,71644298,203665054,579841286,1653025900,
%U 4718011460,13479908926,38548802570,110327691316,315985475588
%N Number of base 8 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, 8) 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,..,8}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%F G.f.: (1 - 21*x^2 + 28*x^3 + 60*x^4 - 96*x^5 - 15*x^6 + 36*x^7) / ((1 - 2*x)*(1 - 3*x + x^3)*(1 - 3*x + 3*x^3)) (conjectured). - _Colin Barker_, Jun 03 2017
%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