OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8,-10).
FORMULA
From Philippe Deléham, Jan 06 2009: (Start)
a(n) = 8*a(n-1) - 10*a(n-2) for n > 1, where a(0)=0, a(1)=1.
G.f.: x/(1 - 8*x + 10*x^2). (End)
MATHEMATICA
LinearRecurrence[{8, -10}, {1, 8}, 30] (* or *) Table[Simplify[((4 + Sqrt[6])^n -(4-Sqrt[6])^n)/(2*Sqrt[6])], {n, 30}] (* G. C. Greubel, Sep 06 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((4+r)^n-(4-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(Sage) [lucas_number1(n, 8, 10) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
(PARI) a(n)=([0, 1; -10, 8]^(n-1)*[1; 8])[1, 1] \\ Charles R Greathouse IV, Sep 07 2016
(PARI) my(x='x+O('x^30)); Vec(x/(1-8*x+10*x^2)) \\ G. C. Greubel, May 21 2019
(GAP) a:=[1, 8];; for n in [3..30] do a[n]:=8*a[n-1]-10*a[n-2]; od; a; # G. C. Greubel, May 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009
Edited by Klaus Brockhaus, Oct 04 2009
STATUS
approved