A095897 - OEIS

%I #36 Apr 26 2024 01:44:49

%S 1,8,48,320,1888,11648,69504,419840,2515456,15116288,90667008,

%T 544194560,3264913408,19591036928,117544157184,705277460480,

%U 4231648116736,25389989101568,152339800915968,914039609753600,5484236586876928

%N Expansion of x*(1+4*x-4*x^2)/((1+2*x)*(1-6*x)*(1-8*x^2)).

%H Vincenzo Librandi, <a href="/A095897/b095897.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,20,-32,-96).

%F a(n) = 4*a(n-1) + 20*a(n-2) - 32*a(n-3) - 96*a(n-4) for n > 4.

%F From _Bruno Berselli_, Aug 04 2011: (Start)

%F G.f.: x*(1+4*x-4*x^2)/((1+2*x)*(1-6*x)*(1-8*x^2)).

%F a(n) = 2^(n-2)*(3^n-1+((-1)^n-1)*(sqrt(2)^(n-1)-1)).

%F a(2k+1) = 2^(2k-1)*(3*9^k-2*2^k+1), a(2k) = 4^(k-1)*(9^k-1). (End)

%t LinearRecurrence[{4,20,-32,-96},{1,8,48,320},30] (* _Harvey P. Dale_, Jun 11 2011 *)

%o (Magma) [Floor(2^(n-2)*(3^n-1+((-1)^n-1)*(Sqrt(2)^(n-1)-1))): n in [1..30]]; // _Vincenzo Librandi_, Aug 05 2011

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Jun 11 2004

%E Edited, corrected and extended by _Robert G. Wilson v_, Jun 16 2004

%E Meaningful name from _Joerg Arndt_, Dec 26 2022