%I #21 Sep 08 2022 08:45:42

%S 53000,350754,648508,946262,1244016,1541770,1839524,2137278,2435032,

%T 2732786,3030540,3328294,3626048,3923802,4221556,4519310,4817064,

%U 5114818,5412572,5710326,6008080,6305834,6603588,6901342,7199096

%N a(n) = 297754*n - 244754.

%C The identity (15780962*n^2-25943924*n+10662963)^2-(2809*n^2-4618*n+1898)*(297754*n-244754)^2=1 can be written as A157759(n)^2-A157757(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157758/b157758.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 a(n) = 2*a(n-1) - a(n-2).

%F G.f.: x*(53000 + 244754*x)/(1-x)^2.

%t LinearRecurrence[{2, -1}, {53000, 350754}, 30]

%o (Magma) I:=[53000, 350754]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

%o (PARI) a(n) = 297754*n - 244754;

%Y Cf. A157757, A157759.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 06 2009