A158317 a(n) = 400*n - 1.

399, 799, 1199, 1599, 1999, 2399, 2799, 3199, 3599, 3999, 4399, 4799, 5199, 5599, 5999, 6399, 6799, 7199, 7599, 7999, 8399, 8799, 9199, 9599, 9999, 10399, 10799, 11199, 11599, 11999, 12399, 12799, 13199, 13599, 13999, 14399, 14799, 15199

Offset

1,1

Comments

The identity (400*n-1)^2-(400*n^2-2*n)*(20)^2=1 can be written as a(n)^2-A158316(n)*(20)^2 = 1.

Links

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

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(20^2*t-2)).

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

Formula

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

G.f.: x*(399+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {399, 799}, 50]

Prog

(Magma) I:=[399, 799]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 400*n - 1.

Crossrefs

Cf. A158316.

Sequence in context: A176911 A202158 A126231 * A227008 A253597 A006972

Adjacent sequences: A158314 A158315 A158316 * A158318 A158319 A158320

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved