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A158221
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a(n) = 169n + 1.
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2
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170, 339, 508, 677, 846, 1015, 1184, 1353, 1522, 1691, 1860, 2029, 2198, 2367, 2536, 2705, 2874, 3043, 3212, 3381, 3550, 3719, 3888, 4057, 4226, 4395, 4564, 4733, 4902, 5071, 5240, 5409, 5578, 5747, 5916, 6085, 6254, 6423, 6592, 6761, 6930, 7099, 7268
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OFFSET
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1,1
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COMMENTS
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The identity (169*n+1)^2 - (169*n^2 + 2*n)*(13)^2 = 1 can be written as a(n)^2 - A158220(n)*(13)^2 = 1. - Vincenzo Librandi, Feb 02 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 15 in the first table at p. 85, case d(t) = t*(13^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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G.f.: x*(170-x)/(1-x)^2. - Vincenzo Librandi, Feb 02 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 02 2012
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MATHEMATICA
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LinearRecurrence[{2, -1}, {170, 339}, 50] (* Vincenzo Librandi, Feb 02 2012 *)
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PROG
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(PARI) a(n)=169*n+1 \\ Charles R Greathouse IV, Dec 28 2011
(MAGMA) I:=[170, 339]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 02 2012
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CROSSREFS
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Cf. A158220.
Sequence in context: A043746 A043762 A043771 * A067781 A043344 A045153
Adjacent sequences: A158218 A158219 A158220 * A158222 A158223 A158224
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 14 2009
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STATUS
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approved
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