A157445 a(n) = 14641*n^2 - 4598*n + 362.

10405, 49730, 118337, 216226, 343397, 499850, 685585, 900602, 1144901, 1418482, 1721345, 2053490, 2414917, 2805626, 3225617, 3674890, 4153445, 4661282, 5198401, 5764802, 6360485, 6985450, 7639697, 8323226, 9036037, 9778130

Offset

1,1

Comments

The identity (14641*n^2 - 4598*n + 362)^2 - (121*n^2 - 38*n + 3)*(1331*n - 209)^2 = 1 can be written as a(n)^2 - A157443(n)*A157444(n)^2 = 1. - 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*(-10405 - 18515*x - 362*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {10405, 49730, 118337}, 40] (* Vincenzo Librandi, Jan 26 2012 *)

Prog

(Magma) I:=[10405, 49730, 118337]; [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
(PARI) for(n=1, 22, print1(14641*n^2 - 4598*n + 362", ")); \\ Vincenzo Librandi, Jan 26 2012

Crossrefs

Cf. A157443, A157444.

Sequence in context: A279946 A031866 A262800 * A010082 A068759 A183787

Adjacent sequences: A157442 A157443 A157444 * A157446 A157447 A157448

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Status

approved