A124713 Number of base 20 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 20, 58, 134, 358, 950, 2596, 7160, 19966, 56078, 158488, 450140, 1283848, 3674600, 10549282, 30365294, 87605806, 253263470, 733498744, 2127803180, 6181574548, 17982188708, 52373316262, 152706201170, 445700295760

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, 20) 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,..,20}. 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