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A124716 Number of base 23 circular n-digit numbers with adjacent digits differing by 1 or less. 0
1, 23, 67, 155, 415, 1103, 3019, 8339, 23287, 65495, 185347, 527099, 1505215, 4313423, 12397963, 35728115, 103195687, 298668263, 865957171, 2514793739, 7313712655, 21298240895, 62096722843, 181245885539, 529545304903 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1

a(n) = T(n, 23) 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,..,23}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

LINKS

Table of n, a(n) for n=0..24.

PROG

(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))

CROSSREFS

Sequence in context: A322414 A031376 A069173 * A139955 A126377 A136064

Adjacent sequences:  A124713 A124714 A124715 * A124717 A124718 A124719

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 28 2006

STATUS

approved

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Last modified April 18 14:43 EDT 2019. Contains 322209 sequences. (Running on oeis4.)