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A157448 a(n) = 2048*n^2 - 128*n + 1. 3

%I

%S 1921,7937,18049,32257,50561,72961,99457,130049,164737,203521,246401,

%T 293377,344449,399617,458881,522241,589697,661249,736897,816641,

%U 900481,988417,1080449,1176577,1276801,1381121,1489537,1602049,1718657,1839361

%N a(n) = 2048*n^2 - 128*n + 1.

%C The identity (2048*n^2 - 128*n + 1)^2 - (16*n^2 - n)*(512*n - 16)^2 = 1 can be written as a(n)^2 - A157446(n)*A157447(n)^2 = 1 (see also second comment at A157446). - _Vincenzo Librandi_, Jan 26 2012

%H Vincenzo Librandi, <a href="/A157448/b157448.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&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). - _Vincenzo Librandi_, Jan 26 2012

%F G.f.: x*(-1921 - 2174*x - x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 26 2012

%t LinearRecurrence[{3,-3,1},{1921,7937,18049},40] (* _Vincenzo Librandi_, Jan 26 2012 *)

%o (Magma) I:=[1921, 7937, 18049]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jan 26 2012

%o (PARI) for(n=1, 22, print1(2048*n^2 - 128*n + 1", ")); \\ _Vincenzo Librandi_, Jan 26 2012

%Y Cf. A157446, A157447.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 01 2009

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Last modified February 1 23:45 EST 2023. Contains 359997 sequences. (Running on oeis4.)