A124708 Number of base 15 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 15, 43, 99, 263, 695, 1891, 5195, 14431, 40383, 113723, 321875, 914903, 2609895, 7468147, 21427259, 61622671, 177588815, 512734699, 1482818915, 4294677703, 12455435063, 36167638627, 105140060555, 305958613855, 891185076095

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, 15) 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,..,15}. 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