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%I #11 Jun 01 2017 12:05:37
%S 1,10,98,946,9282,91090,894050,8775154,86128770,845360146,8297271458,
%T 81438324274,799323090114,7845414405202,77003314367714,
%U 755793144551026,7418164815900930,72809828499516562,714633775022856482
%N Number of base 10 circular n-digit numbers with adjacent digits differing by 8 or less.
%C [Empirical] a(base,n)=a(base-1,n)+F(8) for base>=8.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n
%F Conjectures from _Colin Barker_, Jun 01 2017: (Start)
%F G.f.: (1 - x^2 - 16*x^3) / ((1 - x)*(1 - 9*x - 8*x^2)).
%F a(n) = 1 + ((9-sqrt(113))/2)^n + ((9+sqrt(113))/2)^n for n>0.
%F a(n) = 10*a(n-1) - a(n-2) - 8*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]`-$[(i+1)mod N]`>8)+($[(i+1)mod N]`-$[i]`>8))
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 28 2006
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