A125421 - OEIS

%I #12 Jun 02 2017 12:59:54

%S 1,9,79,681,5987,52649,463087,4073225,35827395,315131721,2771845519,

%T 24380686185,214448408099,1886252068073,16591155401263,

%U 145933007686601,1283602149301635,11290348248219273,99308001030865615

%N Number of base 9 circular n-digit numbers with adjacent digits differing by 7 or less.

%C [Empirical] a(base,n)=a(base-1,n)+F(7) for base>=7.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 - 14*x^3) / ((1 - x)*(1 - 8*x - 7*x^2)).

%F a(n) = 1 + (4-sqrt(23))^n + (4+sqrt(23))^n for n>0.

%F a(n) = 9*a(n-1) - a(n-2) - 7*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]`-$[(i+1)mod N]`>7)+($[(i+1)mod N]`-$[i]`>7))

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006