A124702 Number of base 9 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 9, 25, 57, 149, 389, 1045, 2837, 7789, 21549, 60005, 167957, 472169, 1332249, 3770785, 10701617, 30442909, 86779229, 247817845, 708837797, 2030401509, 5823331109, 16720830525, 48060737357, 138268935049, 398126270889

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, 9) 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,..,9}. 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 - 28*x^2 + 56*x^3 + 63*x^4 - 196*x^5 + 30*x^6 + 108*x^7 - 21*x^8 - 8*x^9) / ((1 - x)*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 4*x + x^2 + 6*x^3 + x^4)) (conjectured). - Colin Barker, Jun 02 2017