A158383 625n + 1.

626, 1251, 1876, 2501, 3126, 3751, 4376, 5001, 5626, 6251, 6876, 7501, 8126, 8751, 9376, 10001, 10626, 11251, 11876, 12501, 13126, 13751, 14376, 15001, 15626, 16251, 16876, 17501, 18126, 18751, 19376, 20001, 20626, 21251, 21876, 22501, 23126

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-A158382(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

G.f.: x*(626-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {626, 1251}, 50]
625*Range[40]+1 (* Harvey P. Dale, Mar 14 2018 *)

Prog

I:=[626, 1251]; [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. A158382.

Sequence in context: A045171 A345513 A345766 * A031728 A031638 A098262

Adjacent sequences: A158380 A158381 A158382 * A158384 A158385 A158386

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved