A124726 Number of base 27 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 27, 79, 183, 491, 1307, 3583, 9911, 27715, 78051, 221159, 629711, 1800371, 5165187, 14862871, 42878543, 123982195, 359207987, 1042568407, 3030781151, 8823230131, 25719643811, 75061264951, 219298798031, 641338650427

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, 27) 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,..,27}. 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: A217966 A255186 A121737 * A126381 A129254 A215782

Adjacent sequences: A124723 A124724 A124725 * A124727 A124728 A124729

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

Status

approved