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31, 127, 287, 511, 799, 1151, 1567, 2047, 2591, 3199, 3871, 4607, 5407, 6271, 7199, 8191, 9247, 10367, 11551, 12799, 14111, 15487, 16927, 18431, 19999, 21631, 23327, 25087, 26911, 28799, 30751, 32767, 34847, 36991, 39199, 41471, 43807, 46207
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OFFSET
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1,1
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COMMENTS
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The identity (32*n^2-1)^2 - (256*n^2-16)*(2*n)^2 = 1 can be written as a(n)^2 - A158562(n)*A005843(n)^2 = 1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: x*(-31-34*x+x^2)/(x-1)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
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MATHEMATICA
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32 Range[40]^2 - 1 (* Harvey P. Dale, Mar 04 2011 *)
CoefficientList[Series[(- 31 - 34 x + x^2) / (x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 11 2013 *)
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PROG
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(MAGMA) [32*n^2-1: n in [1..40]]; // Vincenzo Librandi, Sep 11 2013
(PARI) a(n)=32*n^2-1 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A005843, A158562.
Sequence in context: A095322 A127578 A333245 * A079141 A049203 A065403
Adjacent sequences: A158560 A158561 A158562 * A158564 A158565 A158566
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 21 2009
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EXTENSIONS
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Comment rewritten by R. J. Mathar, Oct 16 2009
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STATUS
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approved
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