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 A156843 279841n^2 - 165048n + 24335. 4

%I #32 Sep 08 2022 08:45:41

%S 24335,139128,813603,2047760,3841599,6195120,9108323,12581208,

%T 16613775,21206024,26357955,32069568,38340863,45171840,52562499,

%U 60512840,69022863,78092568,87721955,97911024,108659775,119968208,131836323

%N 279841n^2 - 165048n + 24335.

%C The identity (279841*n^2-165048*n+24335)^2-(529*n^2-312*n+46)*(12167*n-3588)^2=1 can be written as a(n)^2-A156841(n)*A156846(n)^2=1 for n>0.

%H Vincenzo Librandi, <a href="/A156843/b156843.txt">Table of n, a(n) for n = 0..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.: (24335+66123*x+469224*x^2)/(1-x)^3.

%t LinearRecurrence[{3,-3,1},{24335, 139128, 813603},40]

%o (Magma) I:=[24335, 139128, 813603]; [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^2-165048*n+24335 \\ _Charles R Greathouse IV_, Dec 23 2011

%Y Cf. A156841, A156846, A156849.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Feb 17 2009

%E Edited by _Charles R Greathouse IV_, Jul 25 2010

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)