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

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

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

• OEIS Wiki, Number of base k circular n-digit numbers with adjacent digits differing by d or less