A157510 a(n) = 1000*n + 20.

1020, 2020, 3020, 4020, 5020, 6020, 7020, 8020, 9020, 10020, 11020, 12020, 13020, 14020, 15020, 16020, 17020, 18020, 19020, 20020, 21020, 22020, 23020, 24020, 25020, 26020, 27020, 28020, 29020, 30020, 31020, 32020, 33020, 34020, 35020

Offset

1,1

Comments

The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as A157511(n)^2 - A173089(n)*a(n)^2 = 1 (see also second part of the comment at A173089). - Vincenzo Librandi, Feb 04 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

G.f.: x*(1020-20*x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012

Mathematica

LinearRecurrence[{2, -1}, {1020, 2020}, 50] (* Vincenzo Librandi, Feb 04 2012 *)

Prog

MAGMA) I:=[1020, 2020]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(1000*n + 20", ")); \\ Vincenzo Librandi, Feb 04 2012

Crossrefs

Cf. A157511, A173089.

Sequence in context: A245206 A340872 A104444 * A015160 A102925 A216115

Adjacent sequences: A157507 A157508 A157509 * A157511 A157512 A157513

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2009

Status

approved