A158136 a(n) = 144*n - 1.

143, 287, 431, 575, 719, 863, 1007, 1151, 1295, 1439, 1583, 1727, 1871, 2015, 2159, 2303, 2447, 2591, 2735, 2879, 3023, 3167, 3311, 3455, 3599, 3743, 3887, 4031, 4175, 4319, 4463, 4607, 4751, 4895, 5039, 5183, 5327, 5471, 5615, 5759, 5903, 6047, 6191

Offset

1,1

Comments

The identity (144*n - 1)^2 - (144*n^2 - 2*n)*12^2 = 1 can be written as a(n)^2 - A158135(n)*12^2 = 1. - Vincenzo Librandi, Feb 11 2012

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*(12^2*t-2)).

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

Formula

G.f.: x*(143+x)/(1-x)^2. - Vincenzo Librandi, Feb 11 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 11 2012

Mathematica

144Range[50]-1  (* Harvey P. Dale, Feb 14 2011 *)
LinearRecurrence[{2, -1}, {143, 287}, 50] (* Vincenzo Librandi, Feb 11 2012 *)

Prog

(Magma) I:=[143, 287]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012
(PARI) for(n=1, 40, print1(144*n - 1", ")); \\ Vincenzo Librandi, Feb 11 2012

Crossrefs

Cf. A158135.

Sequence in context: A353059 A176876 A257767 * A153874 A003902 A261074

Adjacent sequences: A158133 A158134 A158135 * A158137 A158138 A158139

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 13 2009

Status

approved