|
%I #33 Feb 18 2017 02:14:34
%S 10,28,80,230,664,1922,5574,16188,47064,136946,398746,1161634,3385486,
%T 9869934,28781908,83948652,244894048,714493794,2084792450,6083620812,
%U 17753709802,51812911858,151218254846,441351052720
%N Number of base 10 n-digit numbers with adjacent digits differing by one or less.
%C [Empirical] a(base,n)=a(base-1,n)+3^(n-1) for base>=n; a(base,n)=a(base-1,n)+3^(n-1)-2 when base=n-1.
%H G. C. Greubel, <a href="/A126364/b126364.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,1,6,-1).
%F G.f.: (1 + 4*x - 22*x^2 + 11*x^3 + 14*x^4 - 3*x^5)/(1 - 6*x + 10*x^2 - x^3 - 6*x^4 + x^5). - Alexander R. Povolotsky_, Aug 18 2011
%F Conjecture: a(n) = 3*a(n-1) - A025565(n), n >= 2. - _Daniel Forgues_, Aug 23 2011
%t CoefficientList[ Series[(1 + 4x - 22x^2 + 11x^3 + 14x^4 - 3x^5)/(1 - 6x + 10x^2 - x^3 - 6x^4 + x^5), {x, 0, 24}], x] (* _Robert G. Wilson v_, Aug 19 2011 *)
%t LinearRecurrence[{6, -10, 1, 6, -1}, {10, 28, 80, 230, 664}, 30] (* _Vincenzo Librandi_, Mar 21 2015 *)
%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))
%o (PARI) Vec((1+4*x-22*x^2+11*x^3+14*x^4-3*x^5)/(1-6*x+10*x^2-x^3-6*x^4+x^5)+O(x^99)) \\ _Charles R Greathouse IV_, Aug 23 2011
%K nonn,base,easy
%O 1,1
%A _R. H. Hardin_, Dec 26 2006
|
