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A144479 a(0)=1, a(1)=3, a(n) = 8*a(n-1) - a(n-2). 1

%I

%S 1,3,23,181,1425,11219,88327,695397,5474849,43103395,339352311,

%T 2671715093,21034368433,165603232371,1303791490535,10264728691909,

%U 80814038044737,636247575665987,5009166567283159,39437084962599285,310487513133511121,2444463020105489683

%N a(0)=1, a(1)=3, a(n) = 8*a(n-1) - a(n-2).

%C A105426 extended backwards.

%H Colin Barker, <a href="/A144479/b144479.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -1).

%F G.f.: (1-5*x)/(1-8*x+x^2). - _Philippe Deléham_, Mar 28 2009

%F a(n) = A001090(n+1)-5*A001090(n). - _R. J. Mathar_, Mar 29 2009

%F a(n) = (((4-sqrt(15))^n*(1+sqrt(15))+(-1+sqrt(15))*(4+sqrt(15))^n))/(2*sqrt(15)). - _Colin Barker_, Oct 12 2015

%t LinearRecurrence[{8, -1}, {1, 3}, 25] (* _Vincenzo Librandi_, Oct 12 2015 *)

%o (PARI) Vec((1-5*x)/(1-8*x+x^2) + O(x^40)) \\ _Colin Barker_, Oct 12 2015

%o (MAGMA) I:=[1,3]; [n le 2 select I[n] else 8*Self(n-1)-Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Oct 12 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 28 2009

%E More terms from _Philippe Deléham_ and _R. J. Mathar_, Mar 28 2009

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)