A157366 a(n) = 686*n + 14.

700, 1386, 2072, 2758, 3444, 4130, 4816, 5502, 6188, 6874, 7560, 8246, 8932, 9618, 10304, 10990, 11676, 12362, 13048, 13734, 14420, 15106, 15792, 16478, 17164, 17850, 18536, 19222, 19908, 20594, 21280, 21966, 22652, 23338, 24024, 24710

Offset

1,1

Comments

The identity (4802*n^2+196*n+1)^2-(49*n^2+2*n)*(686*n+14)^2=1 can be written as A157367(n)^2-A157365(n)*a(n)^2=1.

This formula is the case s=7 of the identity (2*s^4*n^2+4*s^2*n+1)^2-(s^2*n^2+2*n)*(2*s^3*n+2*s)^2=1. - Bruno Berselli, Feb 11 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

G.f.: 14*x*(50-x)/(1-x)^2.

a(n) = 2*a(n-1)-a(n-2).

E.g.f.: 14*((1 + 49*x)*exp(x) - 1). - G. C. Greubel, Feb 02 2018

Mathematica

686*Range[36]+14 (* or *) LinearRecurrence[{2, -1}, {700, 1386}, 50]

Prog

(Magma) I:=[700, 1386, 2072]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 686*n+14.

Crossrefs

Cf. A157365, A157367.

Sequence in context: A243837 A116338 A293203 * A293279 A250530 A200169

Adjacent sequences: A157363 A157364 A157365 * A157367 A157368 A157369

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved