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%I #20 Sep 08 2022 08:45:41
%S 24335,469224,1473795,3038048,5161983,7845600,11088899,14891880,
%T 19254543,24176888,29658915,35700624,42302015,49463088,57183843,
%U 65464280,74304399,83704200,93663683,104182848,115261695,126900224
%N 279841n^2 - 394634n + 139128.
%C The identity (279841*n^2-394634*n+139128)^2-(529*n^2-746*n+263)*(12167*n-8579)^2=1 can be written as a(n)^2-A156842(n)*A156845(n)^2=1.
%H Vincenzo Librandi, <a href="/A156844/b156844.txt">Table of n, a(n) for n = 1..10000</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).
%F G.f.: x*(-24335-396219*x-139128*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{24335,469224,1473795},40]
%t Table[279841n^2-394634n+139128,{n,30}] (* _Harvey P. Dale_, Mar 02 2021 *)
%o (Magma) I:=[24335, 469224, 1473795]; [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)=279841*n^2-394634*n+139128 \\ _Charles R Greathouse IV_, Dec 23 2011
%Y CF. A156842, A156845, A156849.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 17 2009
%E Edited by _Charles R Greathouse IV_, Jul 25 2010
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