A124710 Number of base 17 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 17, 49, 113, 301, 797, 2173, 5981, 16645, 46661, 131629, 373181, 1062481, 3035777, 8700601, 25002473, 72015925, 207858677, 601040317, 1740812621, 5049436441, 14666136521, 42649909681, 124166516801, 361855286617

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, 17) 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,..,17}. 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: A029487 A069129 A176273 * A113867 A049737 A146871

Adjacent sequences: A124707 A124708 A124709 * A124711 A124712 A124713

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved