A158135 a(n) = 144*n^2 - 2*n.

142, 572, 1290, 2296, 3590, 5172, 7042, 9200, 11646, 14380, 17402, 20712, 24310, 28196, 32370, 36832, 41582, 46620, 51946, 57560, 63462, 69652, 76130, 82896, 89950, 97292, 104922, 112840, 121046, 129540, 138322, 147392, 156750, 166396

Offset

1,1

Comments

The identity (144*n - 1)^2 - (144*n^2 - 2*n)*12^2 = 1 can be written as A158136(n)^2 - a(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 (3,-3,1).

Formula

G.f.: x*(-142 - 146*x)/(x-1)^3. - Vincenzo Librandi, Feb 11 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {142, 572, 1290}, 50] (* Vincenzo Librandi, Feb 11 2012 *)

Prog

(Magma) I:=[142, 572, 1290]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012
(PARI) for(n=1, 50, print1(144*n^2 - 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012

Crossrefs

Cf. A158136.

Sequence in context: A035702 A172335 A217531 * A092230 A259422 A219146

Adjacent sequences: A158132 A158133 A158134 * A158136 A158137 A158138

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 13 2009

Status

approved