A158395 729n - 1.

728, 1457, 2186, 2915, 3644, 4373, 5102, 5831, 6560, 7289, 8018, 8747, 9476, 10205, 10934, 11663, 12392, 13121, 13850, 14579, 15308, 16037, 16766, 17495, 18224, 18953, 19682, 20411, 21140, 21869, 22598, 23327, 24056, 24785, 25514, 26243

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-A158394(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

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

G.f.: x*(728+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {728, 1457}, 50]

Prog

(Magma) I:=[728, 1457]; [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. A158394.

Sequence in context: A368590 A023704 A043487 * A184077 A234652 A050219

Adjacent sequences: A158392 A158393 A158394 * A158396 A158397 A158398

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved