Search: id:A033888
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%I A033888
%S A033888 0,3,21,144,987,6765,46368,317811,2178309,14930352,102334155,
%T A033888 701408733,4807526976,32951280099,225851433717,1548008755920,
%U A033888 10610209857723,72723460248141,498454011879264,3416454622906707
%N A033888 Fibonacci(4n).
%C A033888 (x,y)=(a(n),a(n+1)) are solutions of (x+y)^2/(1+xy)=9, the other solutions 
               are in A033890.- Floor van Lamoen (fvlamoen(AT)hotmail.com), Dec 
               10 2001
%C A033888 Sequence A033888 provides half of the solutions to the equation 5*x^2 
               + 4 is a square. The other half are found in A033890. Lim. n-> Inf. 
               a(n)/a(n-1) = phi^4 = (7+3*Sqrt(5))/2. - Gregory V. Richardson (omomom(AT)hotmail.com), 
               Oct 13 2002
%H A033888 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A033888 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A033888 a(n)=7a(n-1)-a(n-2).
%F A033888 a(n) = [(7+3*Sqrt(5))^(n-1) - (7-3*Sqrt(5))^(n-1)] / ((2^(n-1))*Sqrt(5)) 
               - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002
%F A033888 a(n) = sum(k=0, n, F(3n-k)*binomial(n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 07 2004
%F A033888 Lucas(2n) * Lucas(n) * Fibonacci(n). - R. Stephan, Sep 25 2004
%F A033888 G.f.: 3x/(1-7x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 17 2008]
%p A033888 (Mupad) numlib::fibonacci(n*4) $ n = 0..30; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 08 2008
%p A033888 sage: [lucas_number1(n,3,1)*lucas_number2(n,3,1) for n in xrange(0,21)] 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 29 2008
%t A033888 Table[Fibonacci[4*n],{n,0,14}] (Vladimir Orlovsky, Jul 21 2008)
%o A033888 sage: [lucas_number1(n,3,1)*lucas_number2(n,3,1) for n in xrange(0,21)] 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 28 2008
%o A033888 (Other) sage: [fibonacci(4*n) for n in xrange(0, 20)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
%Y A033888 Cf. A000045.
%Y A033888 Fourth column of array A102310.
%Y A033888 Sequence in context: A079753 A137969 A054419 this_sequence A141492 A088088 
               A037761
%Y A033888 Adjacent sequences: A033885 A033886 A033887 this_sequence A033889 A033890 
               A033891
%K A033888 nonn,easy
%O A033888 0,2
%A A033888 N. J. A. Sloane (njas(AT)research.att.com).

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