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A158255

a(n) = 289n + 1.

290, 579, 868, 1157, 1446, 1735, 2024, 2313, 2602, 2891, 3180, 3469, 3758, 4047, 4336, 4625, 4914, 5203, 5492, 5781, 6070, 6359, 6648, 6937, 7226, 7515, 7804, 8093, 8382, 8671, 8960, 9249, 9538, 9827, 10116, 10405, 10694, 10983, 11272, 11561

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OFFSET

1,1

COMMENTS

The identity (289*n+1)^2-(289*n^2+2*n)*(17)^2=1 can be written as a(n)^2-A158254(n)*(17)^2=1.

LINKS

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

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*(17^2*t+2)).

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

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

FORMULA

G.f.: x*(290-x)/(1-x)^2. - Bruno Berselli, Mar 21 2011

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

MATHEMATICA

289Range[50]+1 (* Harvey P. Dale, Mar 21 2011 *)

LinearRecurrence[{2, -1}, {290, 579}, 50]

PROG

(Magma) I:=[290, 579]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

(PARI) a(n)=289*n+1 \\ Charles R Greathouse IV, Mar 22 2011

CROSSREFS