A157516 a(n) = 5000*n^2 - 200*n + 1.

4801, 19601, 44401, 79201, 124001, 178801, 243601, 318401, 403201, 498001, 602801, 717601, 842401, 977201, 1122001, 1276801, 1441601, 1616401, 1801201, 1996001, 2200801, 2415601, 2640401, 2875201, 3120001, 3374801, 3639601

Offset

1,1

Comments

The identity (5000*n^2 - 200*n + 1)^2 - (25*n^2 - n)*(1000*n - 20)^2 = 1 can be written as a(n)^2 - A157514(n)*A157515(n)^2 = 1 (see also the second part of the comment at A157514). - Vincenzo Librandi, Jan 26 2012

Links

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

Vincenzo Librandi, X^2-AY^2=1

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(-4801 - 5198*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {4801, 19601, 44401}, 50] (* Vincenzo Librandi, Jan 26 2012 *)

Prog

(Magma) I:=[4801, 19601, 44401]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(5000*n^2 - 200*n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012

Crossrefs

Cf. A157514, A157515.

Sequence in context: A255412 A254791 A096790 * A157628 A214146 A085322

Adjacent sequences: A157513 A157514 A157515 * A157517 A157518 A157519

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2009

Status

approved