A157924 a(n) = 98*n - 1.

97, 195, 293, 391, 489, 587, 685, 783, 881, 979, 1077, 1175, 1273, 1371, 1469, 1567, 1665, 1763, 1861, 1959, 2057, 2155, 2253, 2351, 2449, 2547, 2645, 2743, 2841, 2939, 3037, 3135, 3233, 3331, 3429, 3527, 3625, 3723, 3821, 3919, 4017, 4115, 4213, 4311

Offset

1,1

Comments

The identity (98n - 1)^2 - (49n^2 - n)*14^2 = 1 can be written as a(n)^2 - A157923(n)*14^2 = 1. - Vincenzo Librandi, Feb 05 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*(7^2*t-1)).

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

Formula

G.f.: x*(x+97)/(x-1)^2. - Vincenzo Librandi, Feb 05 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 05 2012

Mathematica

LinearRecurrence[{2, -1}, {97, 195}, 50] (* Vincenzo Librandi, Feb 05 2012 *)
98*Range[50]-1 (* Harvey P. Dale, Mar 14 2016 *)

Prog

(Magma) I:=[97, 195]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 05 2012
(PARI) for(n=1, 40, print1(98*n - 1", ")); \\ Vincenzo Librandi, Feb 05 2012

Crossrefs

Cf. A157923.

Sequence in context: A142398 A133870 A060329 * A323796 A044429 A044810

Adjacent sequences: A157921 A157922 A157923 * A157925 A157926 A157927

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 09 2009

Status

approved