A124700 Number of base 7 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 7, 19, 43, 111, 287, 763, 2051, 5575, 15271, 42099, 116651, 324591, 906367, 2538331, 7126403, 20049671, 56509639, 159514963, 450865067, 1275778031, 3613401695, 10242581819, 29053799555, 82461727687, 234163952487

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, 7) 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,..,7}. 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

Formula

G.f.: (1 - 2*x)*(1 + 2*x - 11*x^2 - 12*x^3 + 21*x^4 + 6*x^5 - 3*x^6) / ((1 - x)*(1 - 2*x - x^2)*(1 - 4*x + 2*x^2 + 4*x^3 - x^4)) (conjectured). - Colin Barker, Jun 03 2017