A125343 Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less.

1, 6, 34, 186, 1058, 6026, 34354, 195866, 1116738, 6367146, 36302674, 206981946, 1180120418, 6728529866, 38363130994, 218729774426, 1247101396098, 7110426078186, 40540535975314, 231144384189306, 1317884064847778

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

Comments

[Empirical] a(base,n)=a(base-1,n)+A025014(n+1) for base>=4.int(n/2)+1

Links

• OEIS Wiki, Number of base k circular n-digit numbers with adjacent digits differing by d or less

Formula

Conjectures from Colin Barker, Jun 02 2017: (Start)

G.f.: (1 - x^2 - 8*x^3) / ((1 - x)*(1 - 5*x - 4*x^2)).

a(n) = 1 + ((5-sqrt(41))/2)^n + ((5+sqrt(41))/2)^n for n>0.

a(n) = 6*a(n-1) - a(n-2) - 4*a(n-3) for n>3.

(End)