A158397 a(n) = 729n + 1.

730, 1459, 2188, 2917, 3646, 4375, 5104, 5833, 6562, 7291, 8020, 8749, 9478, 10207, 10936, 11665, 12394, 13123, 13852, 14581, 15310, 16039, 16768, 17497, 18226, 18955, 19684, 20413, 21142, 21871, 22600, 23329, 24058, 24787, 25516, 26245

Offset

1,1

Comments

The identity (729*n+1)^2-(729*n^2+2*n)*(27)^2 = 1 can be written as a(n)^2-A158396(n)*(27)^2 = 1.

Links

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

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

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*(27^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: x*(730-x)/(1-x)^2.

a(n) = 2*a(n-1)-a(n-2).

Mathematica

LinearRecurrence[{2, -1}, {730, 1459}, 50]
729*Range[40]+1 (* Harvey P. Dale, Apr 08 2014 *)

Prog

(Magma) I:=[730, 1459]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 729*n + 1.

Crossrefs

Cf. A158396.

Sequence in context: A252526 A044880 A141806 * A031732 A224437 A259322

Adjacent sequences: A158394 A158395 A158396 * A158398 A158399 A158400

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved