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A124712 Number of base 19 circular n-digit numbers with adjacent digits differing by 1 or less. 0

%I

%S 1,19,55,127,339,899,2455,6767,18859,52939,149535,424487,1210059,

%T 3461659,9933055,28577687,82409179,238128539,689345935,1998806327,

%U 5804195179,16876837979,49132180735,143192973047,417751959379

%N Number of base 19 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, 19) 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,..,19}. 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 August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)