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a(n) = 18522*n - 10248.
3

%I #19 Sep 08 2022 08:45:42

%S 8274,26796,45318,63840,82362,100884,119406,137928,156450,174972,

%T 193494,212016,230538,249060,267582,286104,304626,323148,341670,

%U 360192,378714,397236,415758,434280,452802,471324,489846,508368,526890,545412,563934

%N a(n) = 18522*n - 10248.

%C The identity (388962*n^2 - 430416*n + 119071)^2 - (441*n^2 - 488*n + 135)*(18522*n - 10248)^2 = 1 can be written as A157732(n)^2 - A157730(n)*a(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A157731/b157731.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).

%F G.f.: x*(8274 + 10248*x)/(1 - x)^2.

%F a(n) = 2*a(n-1) - a(n-2).

%t LinearRecurrence[{2, -1}, {8274, 26796}, 40]

%t 18522 Range[40] - 10248 (* _Harvey P. Dale_, Nov 03 2017 *)

%o (Magma) I:=[8274, 26796]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

%o (PARI) a(n) = 18522*n - 10248.

%Y Cf. A157730, A157732.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 05 2009