A158394 729n^2 - 2n.

727, 2912, 6555, 11656, 18215, 26232, 35707, 46640, 59031, 72880, 88187, 104952, 123175, 142856, 163995, 186592, 210647, 236160, 263131, 291560, 321447, 352792, 385595, 419856, 455575, 492752, 531387, 571480, 613031, 656040, 700507, 746432

Offset

1,1

Comments

The identity (729*n-1)^2-(729*n^2-2*n)*(27)^2=1 can be written as A158395(n)^2-a(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 (3,-3,1).

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-727-731*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {727, 2912, 6555}, 50]
Table[729n^2-2n, {n, 40}] (* Harvey P. Dale, May 14 2022 *)

Prog

(Magma) I:=[727, 2912, 6555]; [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) = 729*n^2 - 2*n.

Crossrefs

Cf. A158395.

Sequence in context: A103170 A153215 A129117 * A038600 A157430 A215158

Adjacent sequences: A158391 A158392 A158393 * A158395 A158396 A158397

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved