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A158309
361n^2 + 2n.
2
363, 1448, 3255, 5784, 9035, 13008, 17703, 23120, 29259, 36120, 43703, 52008, 61035, 70784, 81255, 92448, 104363, 117000, 130359, 144440, 159243, 174768, 191015, 207984, 225675, 244088, 263223, 283080, 303659, 324960, 346983, 369728
OFFSET
1,1
COMMENTS
The identity (361*n+1)^2-(361*n^2+2*n)*(19)^2=1 can be written as A158310(n)^2-a(n)*(19)^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*(19^2*t+2)).
FORMULA
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(363+359*x)/(1-x)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {363, 1448, 3255}, 50]
PROG
(Magma) I:=[363, 1448, 3255]; [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) = 361*n^2 + 2*n.
CROSSREFS
Cf. A158310.
Sequence in context: A192449 A116285 A031697 * A098251 A115464 A004534
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 16 2009
STATUS
approved