A157921 a(n) = 72*n - 1.

71, 143, 215, 287, 359, 431, 503, 575, 647, 719, 791, 863, 935, 1007, 1079, 1151, 1223, 1295, 1367, 1439, 1511, 1583, 1655, 1727, 1799, 1871, 1943, 2015, 2087, 2159, 2231, 2303, 2375, 2447, 2519, 2591, 2663, 2735, 2807, 2879, 2951, 3023, 3095, 3167, 3239

Offset

1,1

Comments

The identity (72*n - 1)^2 - (36*n^2 - n)*12^2 = 1 can be written as a(n)^2 - A157286(n)*12^2 = 1. - Vincenzo Librandi, Jan 28 2012

Links

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

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

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*(6^2*t-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 28 2012

G.f.: x*(x+71)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012

Mathematica

LinearRecurrence[{2, -1}, {71, 143}, 50] (* Vincenzo Librandi, Jan 28 2012 *)
72*Range[50]-1 (* Harvey P. Dale, Sep 06 2019 *)

Prog

(Magma) I:=[71, 143]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(72*n - 1", ")); \\ Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157286.

Sequence in context: A140732 A025023 A253016 * A033224 A142178 A046004

Adjacent sequences: A157918 A157919 A157920 * A157922 A157923 A157924

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 09 2009

Status

approved