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

%I #27 Mar 17 2024 02:11:02

%S 0,9,729,59040,4781511,387243351,31361929920,2539929080169,

%T 205702893563769,16659394449585120,1349205247522830951,

%U 109268965654899721911,8849437012799354643840,716695129071092826429129,58043456017745719586115609,4700803242308332193648935200

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

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

%H Vincenzo Librandi, <a href="/A154026/b154026.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (81,-1).

%F G.f.: (9*x)/(1 -81*x +x^2). - _Harvey P. Dale_, Sep 15 2011

%t LinearRecurrence[{81,-1},{0,9},20] (* _Harvey P. Dale_, Sep 15 2011 *)

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

%o (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

%Y Cf. A065100, A154021-A154027.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 04 2009

%E More terms from _Harvey P. Dale_, Sep 15 2011