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A157661
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80000n^2 - 800n + 1.
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3
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79201, 318401, 717601, 1276801, 1996001, 2875201, 3914401, 5113601, 6472801, 7992001, 9671201, 11510401, 13509601, 15668801, 17988001, 20467201, 23106401, 25905601, 28864801, 31984001, 35263201, 38702401, 42301601, 46060801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (80000*n^2-800*n+1)^2-(100*n^2-n)*(8000*n-40)^2=1 can be written as a(n)^2-A157659(n)* A157660(n)^2=1. This is the case s=10 of the identity (8*n^2*s^4-8*n*s^2+1)^2 -(n^2*s^2-n)*(8*n*s^3-4*s)^2 = 1. - Vincenzo Librandi, Jan 28 2012
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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
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 28 2012
G.f.: x*(-79201-80798*x-x^2)/(x-1)^3. - Vincenzo Librandi, Jan 28 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {79201, 318401, 717601}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
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PROG
| (MAGMA) I:=[79201, 318401, 717601]; [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 28 2012
(PARI) for(n=1, 40, print1(80000*n^2 - 800*n + 1", ")); \\ Vincenzo Librandi, Jan 28 2012
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CROSSREFS
| Cf. A157659, A157660.
Sequence in context: A180973 A204570 A183640 * A159713 A103873 A146324
Adjacent sequences: A157658 A157659 A157660 * A157662 A157663 A157664
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 04 2009
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