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A158742
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a(n) = 74*n^2 + 1.
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2
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1, 75, 297, 667, 1185, 1851, 2665, 3627, 4737, 5995, 7401, 8955, 10657, 12507, 14505, 16651, 18945, 21387, 23977, 26715, 29601, 32635, 35817, 39147, 42625, 46251, 50025, 53947, 58017, 62235, 66601, 71115, 75777, 80587, 85545, 90651, 95905
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OFFSET
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0,2
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COMMENTS
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The identity (74*n^2 + 1)^2 - (1369*n^2 + 37)*(2*n)^2 = 1 can be written as a(n)^2 - A158741(n)*A005843(n))^2 = 1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..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.: -(1 + 72*x + 75*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 75, 297}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
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PROG
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(MAGMA) I:=[1, 75, 297]; [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 21 2012
(PARI) for(n=0, 40, print1(74*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 21 2012
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CROSSREFS
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Cf. A005843, A158741.
Sequence in context: A098230 A258056 A174685 * A292313 A158765 A226741
Adjacent sequences: A158739 A158740 A158741 * A158743 A158744 A158745
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 25 2009
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EXTENSIONS
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Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009
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STATUS
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approved
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