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1, 77, 305, 685, 1217, 1901, 2737, 3725, 4865, 6157, 7601, 9197, 10945, 12845, 14897, 17101, 19457, 21965, 24625, 27437, 30401, 33517, 36785, 40205, 43777, 47501, 51377, 55405, 59585, 63917, 68401, 73037, 77825, 82765, 87857, 93101, 98497
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OFFSET
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0,2
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COMMENTS
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The identity (76*n^2+1)^2-(1444*n^2+38)*(2*n)^2 = 1 can be written as a(n)^2-A158766(n)*A005843(n)^2 = 1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: -(1+74*x+77*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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LinearRecurrence[{3, -3, 1}, {1, 77, 305}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
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PROG
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(MAGMA) I:=[1, 77, 305]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 21 2012
(PARI) for(n=0, 40, print1(76*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 21 2012
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CROSSREFS
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Cf. A005843, A158766.
Sequence in context: A044790 A029558 A156652 * A158771 A020206 A020304
Adjacent sequences: A158764 A158765 A158766 * A158768 A158769 A158770
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 26 2009
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EXTENSIONS
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Comment rewritten, a(0) added, and formula replaced by R. J. Mathar, Oct 22 2009
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STATUS
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approved
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