A158374 625n - 1.

624, 1249, 1874, 2499, 3124, 3749, 4374, 4999, 5624, 6249, 6874, 7499, 8124, 8749, 9374, 9999, 10624, 11249, 11874, 12499, 13124, 13749, 14374, 14999, 15624, 16249, 16874, 17499, 18124, 18749, 19374, 19999, 20624, 21249, 21874, 22499, 23124

Offset

1,1

Comments

The identity (625*n-1)^2-(625*n^2-2*n)*(25)^2=1 can be written as a(n)^2-A158373(n)*(25)^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*(25^2*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*(624+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {624, 1249}, 50]
625*Range[50]-1 (* Harvey P. Dale, May 26 2018 *)

Prog

(Magma) I:=[624, 1249]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 625*n - 1.

Crossrefs

Cf. A158373.

Sequence in context: A180453 A216843 A043368 * A349031 A006912 A318939

Adjacent sequences: A158371 A158372 A158373 * A158375 A158376 A158377

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved