A158409 a(n) = 900*n - 1.

899, 1799, 2699, 3599, 4499, 5399, 6299, 7199, 8099, 8999, 9899, 10799, 11699, 12599, 13499, 14399, 15299, 16199, 17099, 17999, 18899, 19799, 20699, 21599, 22499, 23399, 24299, 25199, 26099, 26999, 27899, 28799, 29699, 30599, 31499

Offset

1,1

Comments

The identity (900*n - 1)^2 - (900*n^2 - 2*n)*30^2=1 can be written as a(n)^2 - A158408(n)*30^2 = 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*(30^2*t-2)).

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

Formula

a(n) = 2*a(n-1) - a(n-2); a(1)=899, a(2)=1799. - Harvey P. Dale, Dec 08 2011

G.f.: x*(899+x)/(x-1)^2. - Bruno Berselli, Dec 08 2011

Mathematica

900*Range[40]-1 (* or *) LinearRecurrence[{2, -1}, {899, 1799}, 40] (* Harvey P. Dale, Dec 08 2011 *)

Prog

(Magma) I:=[899, 1799]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 12 2012
(PARI) for(n=1, 50, print1(900*n - 1", ")); \\ Vincenzo Librandi, Feb 12 2012

Crossrefs

Cf. A158408.

Sequence in context: A252378 A210129 A158408 * A061044 A344595 A344694

Adjacent sequences: A158406 A158407 A158408 * A158410 A158411 A158412

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved