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A157628 80000n^2 - 120800n + 45601. 3

%I #17 Sep 08 2022 08:45:42

%S 4801,124001,403201,842401,1441601,2200801,3120001,4199201,5438401,

%T 6837601,8396801,10116001,11995201,14034401,16233601,18592801,

%U 21112001,23791201,26630401,29629601,32788801,36108001,39587201,43226401

%N 80000n^2 - 120800n + 45601.

%C The identity (80000*n^2-120800*n+45601)^2-(100*n^2-151*n +57)*(8000*n-6040)^2=1 can be written as a(n)^2-A157626(n)*A157627(n)^2=1.

%H Vincenzo Librandi, <a href="/A157628/b157628.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&amp;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).

%F G.f.: x*(-4801-109598*x-45601*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{4801,124001,403201},40]

%t Rest[CoefficientList[Series[x (-4801-109598x-45601x^2)/(x-1)^3,{x,0,30}],x]] (* _Harvey P. Dale_, Apr 30 2022 *)

%o (Magma) I:=[4801, 124001, 403201]; [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)=80000*n^2-120800*n+45601 \\ _Charles R Greathouse IV_, Dec 27 2011

%Y Cf. A157626, A157627.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 03 2009

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)