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257, 513, 769, 1025, 1281, 1537, 1793, 2049, 2305, 2561, 2817, 3073, 3329, 3585, 3841, 4097, 4353, 4609, 4865, 5121, 5377, 5633, 5889, 6145, 6401, 6657, 6913, 7169, 7425, 7681, 7937, 8193, 8449, 8705, 8961, 9217, 9473, 9729, 9985, 10241, 10497
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (256*n+1)^2-(256*n^2+2*n)*(16)^2=1 can be written as a(n)^2-A158230(n)*(16)^2=1.
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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*(16^2*t+2)).
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
| a(1)=257, a(2)=513, a(n)=2*a(n-1)-a(n-2) [From Harvey P. Dale, Nov 21 2011]
G.f.: x*(257-x)/(x-1)^2 [From Harvey P. Dale, Nov 21 2011]
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MATHEMATICA
| 256Range[50]+1 (* or *) LinearRecurrence[{2, -1}, {257, 513}, 50] (* From Harvey P. Dale, Nov 21 2011 *)
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PROG
| (MAGMA) I:=[257, 513]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 256*n + 1.
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CROSSREFS
| Cf. A158230.
Sequence in context: A062382 A105345 A060261 * A070815 A095321 A100633
Adjacent sequences: A158228 A158229 A158230 * A158232 A158233 A158234
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 14 2009
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