A158002 a(n) = 392*n + 1.

1, 393, 785, 1177, 1569, 1961, 2353, 2745, 3137, 3529, 3921, 4313, 4705, 5097, 5489, 5881, 6273, 6665, 7057, 7449, 7841, 8233, 8625, 9017, 9409, 9801, 10193, 10585, 10977, 11369, 11761, 12153, 12545, 12937, 13329, 13721, 14113, 14505, 14897

Offset

0,2

Comments

The identity (392*n + 1)^2 - (196*n^2 + n)*28^2 = 1 can be written as a(n)^2 - (n*A158223(n))*28^2 = 1. - Vincenzo Librandi, Feb 23 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000 (corrected by Ray Chandler, Jan 19 2019)

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

Formula

G.f.: x*(393-x)/(1-x)^2. - Vincenzo Librandi, Feb 10 2012

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

Mathematica

392Range[40]+1 (* Harvey P. Dale, Jul 24 2011 *)
LinearRecurrence[{2, -1}, {393, 785}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

Prog

(Magma) I:=[393, 785]; [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(392*n + 1", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Sequence in context: A045194 A105210 A256742 * A083752 A047825 A227942

Adjacent sequences: A157999 A158000 A158001 * A158003 A158004 A158005

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Extensions

Extended to a(0)=1 by M. F. Hasler, Jan 04 2014

Status

approved