A124799 Number of base 30 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 30, 88, 204, 548, 1460, 4006, 11090, 31036, 87468, 248018, 706670, 2021738, 5804010, 16711552, 48241364, 139572076, 404612780, 1175026834, 3417771710, 9955368238, 29035695998, 84784671532, 247838482400, 725183659570

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, 30) 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,..,30}. 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: A058903 A254474 A103906 * A126384 A025417 A081807

Adjacent sequences: A124796 A124797 A124798 * A124800 A124801 A124802

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved