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

1,2

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).

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A065100, A154021-A154027.

Sequence in context: A189821 A053933 A145262 * A013714 A069034 A053847

Adjacent sequences: A154023 A154024 A154025 * A154027 A154028 A154029

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 04 2009

Extensions

More terms from Harvey P. Dale, Sep 15 2011

Status

approved