A157370 a(n) = 2401*n^2 - 3822*n + 1520.

99, 3480, 11663, 24648, 42435, 65024, 92415, 124608, 161603, 203400, 249999, 301400, 357603, 418608, 484415, 555024, 630435, 710648, 795663, 885480, 980099, 1079520, 1183743, 1292768, 1406595, 1525224, 1648655, 1776888, 1909923

Offset

1,1

Comments

The identity (2401*n^2-3822*n+1520)^2-(49*n^2-78*n+31)*( 343*n-273)^2=1 can be written as a(n)^2-A157368(n)*A157369(n)^2=1.

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 (3,-3,1).

Formula

a(1)=99, a(2)=3480, a(3)=11663, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Dec 03 2011]

G.f.: x*(1520*x^2 + 3183*x + 99)/(1-x)^3. - Harvey P. Dale, Dec 03 2011

E.g.f.: (1520 - 1421*x + 2401*x^2)*exp(x) - 1520. - G. C. Greubel, Feb 02 2018

Mathematica

Table[2401n^2-3822n+1520, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {99, 3480, 11663}, 40] (* Harvey P. Dale, Dec 03 2011 *)

Prog

(Magma) I:=[99, 3480, 11663]; [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)=2401*n^2-3822*n+1520 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A157368, A157369.

Sequence in context: A174944 A221330 A246247 * A163040 A133319 A196745

Adjacent sequences: A157367 A157368 A157369 * A157371 A157372 A157373

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved