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37, 1406, 5513, 12358, 21941, 34262, 49321, 67118, 87653, 110926, 136937, 165686, 197173, 231398, 268361, 308062, 350501, 395678, 443593, 494246, 547637, 603766, 662633, 724238, 788581, 855662, 925481, 998038, 1073333, 1151366, 1232137
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OFFSET
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0,1
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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 A158742(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 = 0..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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G.f.: -37*(1+35*x+38*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}, {37, 1406, 5513}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
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PROG
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(MAGMA) I:=[37, 1406, 5513]; [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(1369*n^2 + 37", ")); \\ Vincenzo Librandi, Feb 21 2012
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CROSSREFS
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Cf. A005843, A158742.
Sequence in context: A189061 A009981 A097315 * A094490 A009695 A201956
Adjacent sequences: A158738 A158739 A158740 * A158742 A158743 A158744
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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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