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71, 143, 215, 287, 359, 431, 503, 575, 647, 719, 791, 863, 935, 1007, 1079, 1151, 1223, 1295, 1367, 1439, 1511, 1583, 1655, 1727, 1799, 1871, 1943, 2015, 2087, 2159, 2231, 2303, 2375, 2447, 2519, 2591, 2663, 2735, 2807, 2879, 2951, 3023, 3095, 3167, 3239
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OFFSET
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1,1
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COMMENTS
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The identity (72*n-1)^2-(36*n^2-n)*(12)^2=1 can be written as a(n)^2-A157286(n)*(12)^2=1. - Vincenzo Librandi, Jan 28 2012
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LINKS
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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*(6^2*t-1)).
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, Jan 28 2012
G.f.: x*(x+71)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012
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MATHEMATICA
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LinearRecurrence[{2, -1}, {71, 143}, 50] (* Vincenzo Librandi, Jan 28 2012 *)
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PROG
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(MAGMA) I:=[71, 143]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(72*n - 1", ")); \\ Vincenzo Librandi, Jan 28 2012
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CROSSREFS
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Cf. A157286.
Sequence in context: A111092 A140732 A025023 * A033224 A142178 A046004
Adjacent sequences: A157918 A157919 A157920 * A157922 A157923 A157924
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 09 2009
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STATUS
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approved
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