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728, 1457, 2186, 2915, 3644, 4373, 5102, 5831, 6560, 7289, 8018, 8747, 9476, 10205, 10934, 11663, 12392, 13121, 13850, 14579, 15308, 16037, 16766, 17495, 18224, 18953, 19682, 20411, 21140, 21869, 22598, 23327, 24056, 24785, 25514, 26243
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OFFSET
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1,1
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COMMENTS
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The identity (729*n-1)^2-(729*n^2-2*n)*(27)^2=1 can be written as a(n)^2-A158394(n)*(27)^2=1.
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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 15 in the first table at p. 85, case d(t) = t*(27^2*t-2)).
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).
G.f.: x*(728+x)/(1-x)^2.
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MATHEMATICA
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LinearRecurrence[{2, -1}, {728, 1457}, 50]
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PROG
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(MAGMA) I:=[728, 1457]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 729*n - 1.
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CROSSREFS
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Cf. A158394.
Sequence in context: A191345 A023704 A043487 * A184077 A050219 A051383
Adjacent sequences: A158392 A158393 A158394 * A158396 A158397 A158398
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 18 2009
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STATUS
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approved
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