A124701 Number of base 8 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 8, 22, 50, 130, 338, 904, 2444, 6682, 18410, 51052, 142304, 398380, 1119308, 3154558, 8914010, 25246282, 71644298, 203665054, 579841286, 1653025900, 4718011460, 13479908926, 38548802570, 110327691316, 315985475588

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, 8) 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,..,8}. 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 - 21*x^2 + 28*x^3 + 60*x^4 - 96*x^5 - 15*x^6 + 36*x^7) / ((1 - 2*x)*(1 - 3*x + x^3)*(1 - 3*x + 3*x^3)) (conjectured). - Colin Barker, Jun 03 2017