A124703 Number of base 10 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 10, 28, 64, 168, 440, 1186, 3230, 8896, 24688, 68958, 193610, 545958, 1545190, 4387012, 12489224, 35639536, 101914160, 291970654, 837834650, 2407780858, 6928681418, 19961961014, 57573920446, 166216938550, 480300958390

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, 10) 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,..,10}. 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 - 36*x^2 + 96*x^3 + 42*x^4 - 336*x^5 + 175*x^6 + 216*x^7 - 126*x^8 - 32*x^9 + 9*x^10) / ((1 - 6*x + 10*x^2 - x^3 - 6*x^4 + x^5)*(1 - 4*x + 2*x^2 + 5*x^3 - 2*x^4 - x^5)) (conjectured). - Colin Barker, Jun 01 2017