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%I A125396 #12 Jun 02 2017 12:59:46
%S A125396 1,8,62,470,3650,28358,220394,1712894,13312610,103465622,804135002,
%T A125396 6249738734,48572981138,377509300358,2934002989322,22803076727390,
%U A125396 177225555027650,1377397345557878,10705134749071034,83200327316844494
%N A125396 Number of base 8 circular n-digit numbers with adjacent digits differing by 6 or less.
%C A125396 [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 A125396 Conjectures from _Colin Barker_, Jun 02 2017: (Start)
%F A125396 G.f.: (1 - x^2 - 12*x^3) / ((1 - x)*(1 - 7*x - 6*x^2)).
%F A125396 a(n) = 1 + ((7-sqrt(73))/2)^n + ((7+sqrt(73))/2)^n for n>0.
%F A125396 a(n) = 8*a(n-1) - a(n-2) - 6*a(n-3) for n>3.
%F A125396 (End)
%o A125396 (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 A125396 nonn,base
%O A125396 0,2
%A A125396 _R. H. Hardin_, Dec 28 2006

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