A157735 - OEIS

%I #20 Sep 08 2022 08:45:42

%S 10248,28770,47292,65814,84336,102858,121380,139902,158424,176946,

%T 195468,213990,232512,251034,269556,288078,306600,325122,343644,

%U 362166,380688,399210,417732,436254,454776,473298,491820,510342,528864,547386

%N 18522n - 8274.

%C The identity (388962*n^2-347508*n+77617)^2-(441*n^2-394*n+88)*(18522*n- 8274)^2=1 can be written as A157736(n)^2-A157734(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157735/b157735.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*(10248+8274*x)/(x-1)^2.

%t LinearRecurrence[{2,-1},{10248,28770},40]

%o (Magma) I:=[10248, 28770]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

%o (PARI) a(n) = 18522*n - 8274.

%Y Cf. A157734, A157736.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 05 2009