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%I A157757 #19 Aug 02 2024 19:20:19
%S A157757 89,3898,13325,28370,49033,75314,107213,144730,187865,236618,290989,
%T A157757 350978,416585,487810,564653,647114,735193,828890,928205,1033138,
%U A157757 1143689,1259858,1381645,1509050,1642073,1780714,1924973,2074850
%N A157757 a(n) = 2809*n^2 - 4618*n + 1898.
%C A157757 The identity (15780962*n^2-25943924*n+10662963)^2-(2809*n^2-4618*n+1898)*(297754*n-244754)^2=1 can be written as A157759(n)^2-a(n)*A157758(n)^2=1.
%H A157757 Vincenzo Librandi, <a href="/A157757/b157757.txt">Table of n, a(n) for n = 1..10000</a>
%H A157757 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157757 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F A157757 G.f.: x*(-89-3631*x-1898*x^2)/(x-1)^3.
%t A157757 LinearRecurrence[{3,-3,1},{89,3898,13325},40]
%t A157757 Table[2809n^2-4618n+1898,{n,40}] (* _Harvey P. Dale_, Aug 02 2024 *)
%o A157757 (Magma) I:=[89, 3898, 13325]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o A157757 (PARI) a(n) = 2809*n^2 - 4618*n + 1898;
%Y A157757 Cf. A157758, A157759.
%K A157757 nonn,easy
%O A157757 1,1
%A A157757 _Vincenzo Librandi_, Mar 06 2009

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