A157374 a(n) = 343*n - 70.

273, 616, 959, 1302, 1645, 1988, 2331, 2674, 3017, 3360, 3703, 4046, 4389, 4732, 5075, 5418, 5761, 6104, 6447, 6790, 7133, 7476, 7819, 8162, 8505, 8848, 9191, 9534, 9877, 10220, 10563, 10906, 11249, 11592, 11935, 12278, 12621, 12964, 13307, 13650

Offset

1,1

Comments

The identity (2401*n^2-980*n+99)^2-(49*n^2-20*n +2)*(343*n-70)^2=1 can be written as A157375(n)^2-A157373(n)*a(n)^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

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*(70*x+273)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012

E.g.f.: (343*x - 70)*exp(x) + 70. - G. C. Greubel, Feb 02 2018

Mathematica

LinearRecurrence[{2, -1}, {273, 616}, 40] (* Vincenzo Librandi, Jan 28 2012 *)

Prog

(Magma) I:=[273, 616]; [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(343*n-70", ")); \\ Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157373, A153375.

Sequence in context: A347882 A347888 A306812 * A043467 A028530 A200836

Adjacent sequences: A157371 A157372 A157373 * A157375 A157376 A157377

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved