A158313 a(n) = 400 * n + 1.

401, 801, 1201, 1601, 2001, 2401, 2801, 3201, 3601, 4001, 4401, 4801, 5201, 5601, 6001, 6401, 6801, 7201, 7601, 8001, 8401, 8801, 9201, 9601, 10001, 10401, 10801, 11201, 11601, 12001, 12401, 12801, 13201, 13601, 14001, 14401, 14801, 15201

Offset

1,1

Comments

The identity (400*n+1)^2-(00*n^2+2*n)*(20)^2=1 can be written as a(n)^2-A158312(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

G.f.: x*(401-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {401, 801}, 50]
400*Range[40]+1 (* Harvey P. Dale, Jun 01 2018 *)

Prog

(Magma) I:=[401, 801]; [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. A158312.

Sequence in context: A096991 A332674 A141026 * A094614 A104926 A031718

Adjacent sequences: A158310 A158311 A158312 * A158314 A158315 A158316

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved