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%I #13 Jun 01 2017 12:04:50
%S 1,10,28,64,168,440,1186,3230,8896,24688,68958,193610,545958,1545190,
%T 4387012,12489224,35639536,101914160,291970654,837834650,2407780858,
%U 6928681418,19961961014,57573920446,166216938550,480300958390
%N Number of base 10 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, 10) 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,..,10}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%F G.f.: (1 - 36*x^2 + 96*x^3 + 42*x^4 - 336*x^5 + 175*x^6 + 216*x^7 - 126*x^8 - 32*x^9 + 9*x^10) / ((1 - 6*x + 10*x^2 - x^3 - 6*x^4 + x^5)*(1 - 4*x + 2*x^2 + 5*x^3 - 2*x^4 - x^5)) (conjectured). - _Colin Barker_, Jun 01 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
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