A154026 a(n+2) = 81*a(n+1) - a(n), a(1)=0, a(2)=9.

0, 9, 729, 59040, 4781511, 387243351, 31361929920, 2539929080169, 205702893563769, 16659394449585120, 1349205247522830951, 109268965654899721911, 8849437012799354643840, 716695129071092826429129, 58043456017745719586115609, 4700803242308332193648935200

Offset: 1

Author

Vincenzo Librandi, Jan 04 2009

Keywords

• nonn
• easy

Comments

If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=81.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (81,-1).

Crossrefs

Cf. A065100, A154021-A154027.

Programs

Magma

I:=[0,9]; [n le 2 select I[n] else 81*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 25 2012

Mathematica

LinearRecurrence[{81,-1},{0,9},20] (* Harvey P. Dale, Sep 15 2011 *)

PARI

concat(0,Vec(9/(x^2-81*x+1)+O(x^98))) \\ Charles R Greathouse IV, Dec 27 2011

Formula

G.f.: (9*x)/(1 -81*x +x^2). - Harvey P. Dale, Sep 15 2011

Extensions

More terms from Harvey P. Dale, Sep 15 2011