A157990 a(n) = 288*n + 1.

289, 577, 865, 1153, 1441, 1729, 2017, 2305, 2593, 2881, 3169, 3457, 3745, 4033, 4321, 4609, 4897, 5185, 5473, 5761, 6049, 6337, 6625, 6913, 7201, 7489, 7777, 8065, 8353, 8641, 8929, 9217, 9505, 9793, 10081, 10369, 10657, 10945, 11233, 11521

Offset

1,1

Comments

The identity (288*n + 1)^2 - (144*n^2 + n)*24^2 = 1 can be written as a(n)^2 - (A017522(n) + n)*24^2 = 1. - Vincenzo Librandi, Feb 10 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 14 in the first table at p. 85, case d(t) = t*(12^2*t+1)).

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

Formula

G.f.: x*(289-x)/(1-x)^2. - Vincenzo Librandi, Feb 10 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{2, -1}, {289, 577}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

Prog

(Magma) I:=[289, 577]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 50, print1(288*n + 1", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A017522.

Sequence in context: A287934 A152852 A156572 * A261111 A218766 A188186

Adjacent sequences: A157987 A157988 A157989 * A157991 A157992 A157993

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved