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 A157857 a(n) = 3600*n^2 - n. 3

%I

%S 3599,14398,32397,57596,89995,129594,176393,230392,291591,359990,

%T 435589,518388,608387,705586,809985,921584,1040383,1166382,1299581,

%U 1439980,1587579,1742378,1904377,2073576,2249975,2433574,2624373,2822372

%N a(n) = 3600*n^2 - n.

%C The identity (103680000*n^2 - 28800*n + 1)^2 - (3600*n^2 - n)*(1728000*n - 240)^2 = 1 can be written as A157859(n)^2 - a(n)*A157858(n)^2 = 1 (see second comment at A157858). - _Vincenzo Librandi_, Jan 25 2012

%H Vincenzo Librandi, <a href="/A157857/b157857.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 G.f.: x*(3599 + 3601*x)/(1-x)^3. - _Colin Barker_, Jan 17 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 25 2012

%t LinearRecurrence[{3,-3,1},{3599,14398,32397},40] (* _Vincenzo Librandi_, Jan 25 2012 *)

%t Table[3600n^2-n,{n,30}] (* _Harvey P. Dale_, Apr 13 2019 *)

%o (MAGMA) I:=[3599, 14398, 32397]; [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 25 2012

%o (PARI) for(n=1, 30, print1(3600*n^2 - n", ")); \\ _Vincenzo Librandi_, Jan 25 2012

%Y Cf. A157858, A157859.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 08 2009

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)