A158407 a(n) = 900*n + 1.

901, 1801, 2701, 3601, 4501, 5401, 6301, 7201, 8101, 9001, 9901, 10801, 11701, 12601, 13501, 14401, 15301, 16201, 17101, 18001, 18901, 19801, 20701, 21601, 22501, 23401, 24301, 25201, 26101, 27001, 27901, 28801, 29701, 30601, 31501

Offset

1,1

Comments

The identity (900*n + 1)^2 - (900*n^2 + 2*n)*30^2 = 1 can be written as a(n)^2 - A158406(n)*(30)^2 = 1. - Vincenzo Librandi, Feb 09 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*(901-x)/(1-x)^2. - Vincenzo Librandi, Feb 09 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 09 2012

Mathematica

LinearRecurrence[{2, -1}, {901, 1801}, 50] (* Vincenzo Librandi, Feb 09 2012 *)
900*Range[40]+1 (* Harvey P. Dale, Aug 18 2019 *)

Prog

(Magma) I:=[901, 1801]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 09 2012
(PARI) for(n=1, 40, print1(900*n + 1", ")); \\ Vincenzo Librandi, Feb 09 2012

Crossrefs

Cf. A158406.

Sequence in context: A093218 A093215 A252674 * A250782 A031738 A268585

Adjacent sequences: A158404 A158405 A158406 * A158408 A158409 A158410

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved