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(MAGMAMagma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)^n-(4-r)^n)/(2*r): n in [1..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
(MAGMAMagma) I:=[1, 8]; [n le 2 select I[n] else 8*Self(n-1)-13*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016
(Sage) [lucas_number1(n, 8, 13) for n in xrangerange(1, 22)] # Zerinvary Lajos, Apr 23 2009
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lim_Lim_{n -> infinity} a(n)/a(n-1) = 4 + sqrt(3) = 5.73205080756887729....
G.f.: x/(1 - 8*x + 13*x^2). - Klaus Brockhaus, Dec 31 2008, corrected Oct 11 2009
a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
Join[{a=1, b=8}, Table[c=8*b-13*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *)
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G.f.: x/(1-8*x+13*x^2). [_- _Klaus Brockhaus_, Dec 31 2008, corrected Oct 11 2009]
(PARI) a(n)=([0, 1; -13, 8]^(n-1)*[1; 8])[1, 1] \\ Charles R Greathouse IV, Sep 04 2016
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