A124712 Number of base 19 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 19, 55, 127, 339, 899, 2455, 6767, 18859, 52939, 149535, 424487, 1210059, 3461659, 9933055, 28577687, 82409179, 238128539, 689345935, 1998806327, 5804195179, 16876837979, 49132180735, 143192973047, 417751959379

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, 19) 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,..,19}. 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: A044121 A044502 A069131 * A126373 A125818 A362298

Adjacent sequences: A124709 A124710 A124711 * A124713 A124714 A124715

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved