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A124714 Number of base 21 circular n-digit numbers with adjacent digits differing by 1 or less. 0

%I

%S 1,21,61,141,377,1001,2737,7553,21073,59217,167441,475793,1357637,

%T 3887541,11165509,32152901,92802433,268398401,777651553,2256800033,

%U 6558953917,19087539437,55614451789,162219429293,473648632141

%N Number of base 21 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, 21) 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,..,21}. 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 October 6 20:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)