A158401 a(n) = 841*n^2 - 2*n.

839, 3360, 7563, 13448, 21015, 30264, 41195, 53808, 68103, 84080, 101739, 121080, 142103, 164808, 189195, 215264, 243015, 272448, 303563, 336360, 370839, 407000, 444843, 484368, 525575, 568464, 613035, 659288, 707223, 756840, 808139, 861120

Offset

1,1

Comments

The identity (841*n-1)^2-(841*n^2-2*n)*(29)^2 = 1 can be written as A158402(n)^2-a(n)*(29)^2 = 1.

Links

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(29^2*t-2)).

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) for n > 3.

G.f.: x*(-839-843*x)/(x-1)^3.

Maple

A158401:=n->841*n^2 - 2*n: seq(A158401(n), n=1..50); # Wesley Ivan Hurt, Oct 15 2017

Mathematica

LinearRecurrence[{3, -3, 1}, {839, 3360, 7563}, 50]
Table[841n^2-2n, {n, 40}] (* Harvey P. Dale, Jan 31 2023 *)

Prog

(Magma) I:=[839, 3360, 7563]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 841*n^2 - 2*n.

Crossrefs

Cf. A158402.

Sequence in context: A118380 A351671 A135639 * A290119 A156937 A135640

Adjacent sequences: A158398 A158399 A158400 * A158402 A158403 A158404

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved