A124716 Number of base 23 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 23, 67, 155, 415, 1103, 3019, 8339, 23287, 65495, 185347, 527099, 1505215, 4313423, 12397963, 35728115, 103195687, 298668263, 865957171, 2514793739, 7313712655, 21298240895, 62096722843, 181245885539, 529545304903

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, 23) 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,..,23}. 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