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%I #22 May 14 2018 18:20:27
%S 1,10,80,580,4660,37960,311378,2559658,21057948,173287588,1426133270,
%T 11737272106,96600478510,795047628502,6543462720560,53854541701240,
%U 443238127915788,3647975524214452,30023874009147704,247105006940966092
%N Number of base 10 circular n-digit numbers with adjacent digits differing by 5 or less.
%C [Empirical] a(base,n)=a(base-1,n)+F(5) for base>=5.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (11, -21, -19, 34, 8, -15, -1, 2).
%F G.f.: (1 - x - 9*x^2 - 71*x^3 + 116*x^4 + 52*x^5 - 87*x^6 - 9*x^7 + 16*x^8)/((1 + x)(1 - 3*x + x^3)(1 - 9*x + 6*x^2 + 3*x^3 - 2*x^4)). For n<4, a(n) = 5*6^n-4*5^n = A257286(n). - _M. F. Hasler_, May 03 2015
%t LinearRecurrence[{11,-21,-19,34,8,-15,-1,2},{1,10,80,580,4660,37960,311378,2559658,21057948},30] (* _Harvey P. Dale_, May 14 2018 *)
%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>5)+($[(i+1)mod N]`-$[i]`>5))
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 28 2006