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A124713 Number of base 20 circular n-digit numbers with adjacent digits differing by 1 or less. 0

%I

%S 1,20,58,134,358,950,2596,7160,19966,56078,158488,450140,1283848,

%T 3674600,10549282,30365294,87605806,253263470,733498744,2127803180,

%U 6181574548,17982188708,52373316262,152706201170,445700295760

%N Number of base 20 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, 20) 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,..,20}. 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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Last modified September 24 16:57 EDT 2022. Contains 356943 sequences. (Running on oeis4.)