%I #12 Jun 02 2017 12:59:46

%S 1,8,62,470,3650,28358,220394,1712894,13312610,103465622,804135002,

%T 6249738734,48572981138,377509300358,2934002989322,22803076727390,

%U 177225555027650,1377397345557878,10705134749071034,83200327316844494

%N Number of base 8 circular n-digit numbers with adjacent digits differing by 6 or less.

%C [Empirical] a(base,n)=a(base-1,n)+F(6) for base>=6.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n

%F Conjectures from _Colin Barker_, Jun 02 2017: (Start)

%F G.f.: (1 - x^2 - 12*x^3) / ((1 - x)*(1 - 7*x - 6*x^2)).

%F a(n) = 1 + ((7-sqrt(73))/2)^n + ((7+sqrt(73))/2)^n for n>0.

%F a(n) = 8*a(n-1) - a(n-2) - 6*a(n-3) for n>3.

%F (End)

%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>6)+($[(i+1)mod N]`-$[i]`>6))

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006