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127, 255, 383, 511, 639, 767, 895, 1023, 1151, 1279, 1407, 1535, 1663, 1791, 1919, 2047, 2175, 2303, 2431, 2559, 2687, 2815, 2943, 3071, 3199, 3327, 3455, 3583, 3711, 3839, 3967, 4095, 4223, 4351, 4479, 4607, 4735, 4863, 4991, 5119, 5247, 5375, 5503
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (128*n-1)^2-(64*n^2-n)*(16)^2=1 can be written as a(n)^2-A157948(n)*(16)^2=1. - Vincenzo Librandi, Jan 29 2012
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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 14 in the first table at p. 85, case d(t) = t*(8^2*t-1)).
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
| a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, Jan 29 2012
G.f.: x*(127+x)/(1-x)^2. - Vincenzo Librandi, Jan 29 2012
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MATHEMATICA
| LinearRecurrence[{2, -1}, {127, 255}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (MAGMA) I:=[127, 255]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(128*n - 1", ")); \\ Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| Cf. A157948.
Sequence in context: A048453 A196657 A138127 * A142165 A031933 A080035
Adjacent sequences: A157946 A157947 A157948 * A157950 A157951 A157952
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009
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