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%I #18 Sep 08 2022 08:45:41
%S 3395619,17808513,43524451,80543433,128865459,188490529,259418643,
%T 341649801,435184003,540021249,656161539,783604873,922351251,
%U 1072400673,1233753139,1406408649,1590367203,1785628801,1992193443,2210061129
%N 5651522n^2 - 2541672n + 285769.
%C The identity (5651522*n^2-2541672*n+285769)^2-(1681*n^2-756*n+85)*(137842*n-30996)^2=1 can be written as a(n)^2-A157010(n)*A157105(n)^2=1.
%H Vincenzo Librandi, <a href="/A157106/b157106.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">X^2-AY^2=1</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%p A157106:=n->5651522*n^2 - 2541672*n + 285769; seq(A157106(n), n=1..30); # _Wesley Ivan Hurt_, Jan 23 2014
%t LinearRecurrence[{3,-3,1},{3395619,17808513,43524451},30]
%o (Magma) I:=[3395619, 17808513, 43524451]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n) = 5651522*n^2 - 2541672*n + 285769.
%Y Cf. A157010, A157105.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 23 2009
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