A125372 - OEIS

%I #35 Oct 16 2017 17:04:34

%S 1,9,69,489,3773,29359,229371,1793675,14030597,109759917,858660839,

%T 6717419531,52551380915,411117567181,3216236722495,25161121675789,

%U 196839383096437,1539905230937741,12046919094905577,94244929368967819

%N Number of base-9 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*floor(n/2) + 1 and F(d) is the largest coefficient in (1 + x + ... + x^(2d))^n.

%H Vincenzo Librandi, <a href="/A125372/b125372.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (9,-6,-26,5,17,-1,-3).

%F G.f.: (1 - 6*x^2 - 52*x^3 + 15*x^4 + 68*x^5 - 5*x^6 - 18*x^7)/((1 + x)*(1 - 2*x - x^2 + x^3)*(1 - 8*x + x^2 + 3*x^3)). - _M. F. Hasler_, May 03 2015

%F For n < 4, a(n) = 4*6^n - 3*5^n. - _M. F. Hasler_, May 03 2015

%F a(n) = 9*a(n-1) - 6*a(n-2) - 26*a(n-3) + 5*a(n-4) + 17*a(n-5) - a(n-6) - 3*a(n-7) for n > 7. - _Wesley Ivan Hurt_, Oct 08 2017

%t CoefficientList[Series[(1 - 6*x^2 - 52*x^3 + 15*x^4 + 68*x^5 - 5*x^6 - 18*x^7)/((1 + x)*(1 - 2*x - x^2 + x^3)*(1 - 8*x + x^2 + 3*x^3)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Oct 08 2017 *)

%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