A124711 Number of base 18 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 18, 52, 120, 320, 848, 2314, 6374, 17752, 49800, 140582, 398834, 1136270, 3248718, 9316828, 26790080, 77212552, 222993608, 645193126, 1869809474, 5426815810, 15771487250, 45891045208, 133679744924, 389803622998

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, 18) 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,..,18}. 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: A175815 A069130 A299071 * A126372 A334645 A133356

Adjacent sequences: A124708 A124709 A124710 * A124712 A124713 A124714

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved