0,2

(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

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

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

a(n)=7a(n-1)-a(n-2).

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

a(n) = sum(k=0, n, F(3n-k)*binomial(n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 07 2004

Lucas(2n) * Lucas(n) * Fibonacci(n). - R. Stephan, Sep 25 2004

G.f.: 3x/(1-7x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

(Mupad) numlib::fibonacci(n*4) $ n = 0..30; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008

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

Table[Fibonacci[4*n], {n, 0, 14}] (Vladimir Orlovsky, Jul 21 2008)

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

(Other) sage: [fibonacci(4*n) for n in xrange(0, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]

Cf. A000045.

Fourth column of array A102310.

Sequence in context: A079753 A137969 A054419 this_sequence A141492 A088088 A037761

Adjacent sequences: A033885 A033886 A033887 this_sequence A033889 A033890 A033891

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).