OFFSET
1,2
COMMENTS
First differences are in A164588.
Lim_{n -> infinity} a(n)/a(n-1) = 5 + 2*sqrt(2) = 7.8284271247....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (10, -17).
FORMULA
a(n) = 10*a(n-1) - 17*a(n-2) for n > 1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009
G.f.: x/(1 - 10*x + 17*x^2). - Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009
E.g.f.: (1/sqrt(8))*exp(5*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 11 2016
MAPLE
A154340:=n->((5+2*sqrt(2))^n-(5-2*sqrt(2))^n)/(4*sqrt(2)): seq(simplify(A154340(n)), n=1..30); # Wesley Ivan Hurt, Sep 12 2016
MATHEMATICA
Drop[CoefficientList[Series[x/(1-10*x+17*x^2), {x, 0, 30}], x], 1] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011, modified by G. C. Greubel, Jun 01 2019 *)
LinearRecurrence[{10, -17}, {1, 10}, 30] (* or *) Table[Simplify[((5 + 2*Sqrt[2])^n -(5-2*Sqrt[2])^n)/(4*Sqrt[2])], {n, 1, 30}] (* G. C. Greubel, Sep 11 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)^n-(5-2*r)^n)/(4*r): n in [1..30] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009
(Sage) [lucas_number1(n, 10, 17) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009
(Magma) I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 12 2016
(PARI) a(n)=([0, 1; -17, 10]^(n-1)*[1; 10])[1, 1] \\ Charles R Greathouse IV, Sep 12 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
STATUS
approved