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A158627
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a(n) = 484*n^2-22.
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2
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462, 1914, 4334, 7722, 12078, 17402, 23694, 30954, 39182, 48378, 58542, 69674, 81774, 94842, 108878, 123882, 139854, 156794, 174702, 193578, 213422, 234234, 256014, 278762, 302478, 327162, 352814, 379434, 407022, 435578, 465102, 495594
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OFFSET
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1,1
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COMMENTS
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The identity (44*n^2-1)^2 - (484*n^2-22)*(2*n)^2 = 1 can be written as A158628(n)^2 - a(n)*A005843(n)^2 = 1.
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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
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: 22*x*(-21-24*x+x^2)/(x-1)^3. - Vincenzo Librandi, Feb 17 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 17 2012
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {462, 1914, 4334}, 50] (* Vincenzo Librandi, Feb 17 2012 *)
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PROG
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(Magma) I:=[462, 1914, 4334]; [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 17 2012
(PARI) for(n=1, 40, print1(484*n^2-22", ")); \\ Vincenzo Librandi, Feb 17 2012
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CROSSREFS
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Cf. A005843, A158628.
Sequence in context: A222342 A246476 A202642 * A267567 A267557 A154056
Adjacent sequences: A158624 A158625 A158626 * A158628 A158629 A158630
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 23 2009
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EXTENSIONS
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Edited by R. J. Mathar, Jul 26 2009
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STATUS
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approved
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