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A157732
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388962n^2 - 430416n + 119071.
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3
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77617, 814087, 2328481, 4620799, 7691041, 11539207, 16165297, 21569311, 27751249, 34711111, 42448897, 50964607, 60258241, 70329799, 81179281, 92806687, 105212017, 118395271, 132356449, 147095551, 162612577, 178907527
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OFFSET
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1,1
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COMMENTS
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The identity (388962*n^2-430416*n+119071)^2-(441*n^2-488*n+135)*(18522*n-10248)^2=1 can be written as a(n)^2-A157730(n)*A157731(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 to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-77617-581236*x-119071*x^2)/(x-1)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {77617, 814087, 2328481}, 40]
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PROG
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(MAGMA) I:=[77617, 814087, 2328481]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 388962*n^2 - 430416*n + 119071.
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CROSSREFS
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Cf. A157730, A157731.
Sequence in context: A215662 A183694 A206275 * A210123 A069044 A087026
Adjacent sequences: A157729 A157730 A157731 * A157733 A157734 A157735
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 05 2009
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STATUS
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approved
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