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398, 1596, 3594, 6392, 9990, 14388, 19586, 25584, 32382, 39980, 48378, 57576, 67574, 78372, 89970, 102368, 115566, 129564, 144362, 159960, 176358, 193556, 211554, 230352, 249950, 270348, 291546, 313544, 336342, 359940, 384338, 409536
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OFFSET
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1,1
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COMMENTS
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The identity (400*n-1)^2-(400*n^2-2*n)*(20)^2=1 can be written as A158317(n)^2-a(n)*(20)^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
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(20^2*t-2)).
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*(-398-402*x)/(x-1)^3.
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {398, 1596, 3594}, 50]
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PROG
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(MAGMA) I:=[398, 1596, 3594]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 400*n^2 - 2*n.
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CROSSREFS
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Cf. A158317.
Sequence in context: A129190 A152309 A191942 * A187515 A046013 A176911
Adjacent sequences: A158313 A158314 A158315 * A158317 A158318 A158319
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 16 2009
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STATUS
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approved
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