A157739 a(n) = 388962*n^2 - 1764*n + 1.

387199, 1552321, 3495367, 6216337, 9715231, 13992049, 19046791, 24879457, 31490047, 38878561, 47044999, 55989361, 65711647, 76211857, 87489991, 99546049, 112380031, 125991937, 140381767, 155549521, 171495199, 188218801

Offset

1,1

Comments

The identity (388962*n^2 - 1764*n + 1)^2 - (441*n^2 - 2*n)*(18522*n - 42)^2 = 1 can be written as a(n)^2 - A157737(n)*A157738(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

This is the case s=21 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Feb 05 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(-387199 - 390724*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 25 2012

a(n) = 2*A158319(n)^2 - 1. - Bruno Berselli, Feb 05 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {387199, 1552321, 3495367}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

Prog

(Magma) I:=[387199, 1552321, 3495367]; [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
(PARI) for(n=1, 22, print1(388962*n^2-1764*n+1", "));  \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157737, A157738, A158319.

Sequence in context: A206381 A234216 A258686 * A233491 A319505 A106778

Adjacent sequences: A157736 A157737 A157738 * A157740 A157741 A157742

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved