A157815 a(n) = 8984250*n - 330.

8983920, 17968170, 26952420, 35936670, 44920920, 53905170, 62889420, 71873670, 80857920, 89842170, 98826420, 107810670, 116794920, 125779170, 134763420, 143747670, 152731920, 161716170, 170700420, 179684670, 188668920, 197653170

Offset

1,1

Comments

The identity (1482401250*n^2-108900*n+1)^2-(27225*n^2-2*n)*(8984250*n-330)^2=1 can be written as A157816(n)^2-A157814(n)*a(n)^2=1.

Links

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

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

Formula

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

G.f.: x*(8983920+330*x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {8983920, 17968170}, 50]
8984250*Range[30]-330 (* Harvey P. Dale, Mar 13 2018 *)

Prog

(Magma) I:=[8983920, 17968170]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 8984250*n - 330;

Crossrefs

Cf. A157814, A157816.

Sequence in context: A337963 A234192 A162021 * A157821 A106787 A105012

Adjacent sequences: A157812 A157813 A157814 * A157816 A157817 A157818

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved