A157263 a(n) = 1728*n - 1320.

408, 2136, 3864, 5592, 7320, 9048, 10776, 12504, 14232, 15960, 17688, 19416, 21144, 22872, 24600, 26328, 28056, 29784, 31512, 33240, 34968, 36696, 38424, 40152, 41880, 43608, 45336, 47064, 48792, 50520, 52248, 53976, 55704, 57432, 59160

Offset

1,1

Comments

The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as A157264(n)^2-A157262(n)*a(n)^2=1. - Vincenzo Librandi, Jan 27 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

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

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 27 2012

G.f.: x*(408+1320*x)/(x-1)^2. - Vincenzo Librandi, Jan 27 2012

E.g.f.: (1728*x - 1320)*exp(x) + 1320. - G. C. Greubel, Feb 04 2018

Mathematica

LinearRecurrence[{2, -1}, {408, 2136}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
1728*Range[40]-1320 (* Harvey P. Dale, Aug 09 2012 *)

Prog

(Magma) I:=[408, 2136]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 27 2012
(PARI) for(n=1, 40, print1(1728*n - 1320", ")); \\ Vincenzo Librandi, Jan 27 2012

Crossrefs

Cf. A157262, A157264.

Sequence in context: A063145 A281859 A067674 * A234702 A234697 A337795

Adjacent sequences: A157260 A157261 A157262 * A157264 A157265 A157266

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 26 2009

Status

approved