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 A122690 a(0)=1, a(1)=4, a(n)=5*a(n-1)+4*a(n-2) for n>1. 6

%I

%S 1,4,24,136,776,4424,25224,143816,819976,4675144,26655624,151978696,

%T 866515976,4940494664,28168537224,160604664776,915697472776,

%U 5220906022984,29767320006024,169720224122056,967670400634376

%N a(0)=1, a(1)=4, a(n)=5*a(n-1)+4*a(n-2) for n>1.

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (5,4).

%H Harvey P. Dale, <a href="/A122690/b122690.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n)=Sum_{k, 0<=k<=n} 4^k*A122542(n,k) . G.f. (1-x)/(1-5*x-4*x^2). a(n+1)/a(n)-> (5+sqrt(41))/2 = 5.701562118716...if n-> infinity.

%F a(n)=(1/2)*[5/2-(1/2)*sqrt(41)]^n+(3/82)*sqrt(41)*[5/2+(1/2)*sqrt(41)]^n-(3/82)*sqrt(41)*[5/2-(1 /2)*sqrt(41)]^n+(1/2)*[5/2+(1/2)*sqrt(41)]^n, with n>=0 - _Paolo P. Lava_, Jul 07 2008

%t LinearRecurrence[{5,4},{1,4},30] (* From Harvey P. Dale, Apr 06 2012 *)

%o (PARI) Vec((1-x)/(1-5*x-4*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 17 2012

%K nonn,easy,less,changed

%O 0,2

%A _Philippe DELEHAM_, Sep 22 2006

%E Corrected by _T. D. Noe_, Nov 07 2006

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