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%I #10 Aug 13 2012 11:19:53
%S 1,16,46,106,282,746,2032,5588,15538,43522,122676,347528,988692,
%T 2822836,8084374,23214866,66819298,192723746,556887508,1611815768,
%U 4672057072,13560785792,39408774154,114653288678,333906950236
%N Number of base 16 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, 16) 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,..,16}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%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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