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A158364
529n^2 - 2n.
2
527, 2112, 4755, 8456, 13215, 19032, 25907, 33840, 42831, 52880, 63987, 76152, 89375, 103656, 118995, 135392, 152847, 171360, 190931, 211560, 233247, 255992, 279795, 304656, 330575, 357552, 385587, 414680, 444831, 476040, 508307, 541632
OFFSET
1,1
COMMENTS
The identity (529*n-1)^2-(529*n^2-2*n)*(23)^2=1 can be written as A158365(n)^2-a(n)*(23)^2=1.
LINKS
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*(23^2*t-2)).
FORMULA
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-527-531*x)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {527, 2112, 4755}, 50]
PROG
(Magma) I:=[527, 2112, 4755]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 529*n^2 - 2*n.
CROSSREFS
Cf. A158365.
Sequence in context: A337779 A261075 A250754 * A232885 A085329 A157475
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 17 2009
STATUS
approved