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A157739
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388962n^2 - 1764n + 1.
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3
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387199, 1552321, 3495367, 6216337, 9715231, 13992049, 19046791, 24879457, 31490047, 38878561, 47044999, 55989361, 65711647, 76211857, 87489991, 99546049, 112380031, 125991937, 140381767, 155549521, 171495199, 188218801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (388962*n^2-1764*n+1)^2-(441*n^2-2*n)*(18522*n-42)^2=1 can be written as a(n)^2-A157737(n)*A157738(n)^2=1. - Vincenzo Librandi, Jan 25 2012
This is the case s=21 of the identity (2*s^4*n^2-4*s^2*n+1)^2-(s^2*n^2-2*n)*(2*s^3*n-2*s)^2=1. - Bruno Berselli, Feb 05 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..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
| G.f.: x*(-387199-390724*x-x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 25 2012
a(n) = 2*A158319(n)^2-1. - Bruno Berselli, Feb 05 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {387199, 1552321, 3495367}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
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PROG
| (MAGMA) I:=[387199, 1552321, 3495367]; [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, Jan 25 2012
(PARI) for(n=1, 22, print1(388962*n^2-1764*n+1", ")); \\ Vincenzo Librandi, Jan 25 2012
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CROSSREFS
| Cf. A157737, A157738.
Sequence in context: A157843 A206167 A206381 * A106778 A016820 A016856
Adjacent sequences: A157736 A157737 A157738 * A157740 A157741 A157742
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 05 2009
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