OFFSET
1,2
COMMENTS
First differences are in A164551.
Lim_{n -> infinity} a(n)/a(n-1) = 5 + sqrt(6) = 7.4494897427....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..999
Index entries for linear recurrences with constant coefficients, signature (10, -19).
FORMULA
From Philippe Deléham, Jan 06 2009: (Start)
a(n) = 10*a(n-1) - 19*a(n-2) for n > 1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 10*x + 19*x^2). (End)
MATHEMATICA
LinearRecurrence[{10, -19}, {1, 10}, 25] (* or *) Table[Simplify[((5 + Sqrt[6])^n -(5-Sqrt[6])^n)/(2*Sqrt[6])], {n, 1, 25}] (* G. C. Greubel, Sep 06 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((5+r)^n-(5-r)^n)/(2*r): n in [1..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(Sage) [lucas_number1(n, 10, 19) for n in range(1, 25)] # Zerinvary Lajos, Apr 26 2009
(PARI) a(n)=([0, 1; -19, 10]^(n-1)*[1; 10])[1, 1] \\ Charles R Greathouse IV, Sep 07 2016
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