The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A157840 103680000n^2 - 174211200n + 73180801. 3

%I

%S 2649601,139478401,483667201,1035216001,1794124801,2760393601,

%T 3934022401,5315011201,6903360001,8699068801,10702137601,12912566401,

%U 15330355201,17955504001,20788012801,23827881601,27075110401,30529699201

%N 103680000n^2 - 174211200n + 73180801.

%C The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as a(n)^2-A157838(n)*A157839(n)^2=1.

%H Vincenzo Librandi, <a href="/A157840/b157840.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).

%F G.f.: x*(-2649601-131529598*x-73180801*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{2649601,139478401,483667201},40]

%o (MAGMA) I:=[2649601, 139478401, 483667201]; [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) = 103680000*n^2 - 174211200*n + 73180801.

%Y Cf. A157838, A157839.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 09:52 EST 2020. Contains 338876 sequences. (Running on oeis4.)