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A158253 289n - 1. 2
288, 577, 866, 1155, 1444, 1733, 2022, 2311, 2600, 2889, 3178, 3467, 3756, 4045, 4334, 4623, 4912, 5201, 5490, 5779, 6068, 6357, 6646, 6935, 7224, 7513, 7802, 8091, 8380, 8669, 8958, 9247, 9536, 9825, 10114, 10403, 10692, 10981, 11270, 11559 (list; graph; refs; listen; history; text; internal format)
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-A158252(n)*(17)^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*(17^2*t-2)).
FORMULA
a(n) = 2*a(n-1)-a(n-2).
G.f.: x*(288+x)/(1-x)^2.
MATHEMATICA
289Range[50]-1 (* Harvey P. Dale, Nov 01 2011 *)
LinearRecurrence[{2, -1}, {288, 577}, 50]
PROG
(Magma) I:=[288, 577]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 289*n - 1.
CROSSREFS
Cf. A158252.
Sequence in context: A250774 A082994 A127350 * A292054 A250788 A179646
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 15 2009
STATUS
approved

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Last modified June 12 11:18 EDT 2024. Contains 373331 sequences. (Running on oeis4.)