%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