A124718 Number of base 25 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 25, 73, 169, 453, 1205, 3301, 9125, 25501, 71773, 203253, 578405, 1652793, 4739305, 13630417, 39303329, 113588941, 328938125, 954262789, 2772787445, 8068471393, 23508942353, 68578993897, 200272341785, 585441977665

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, 25) 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,..,25}. 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