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29, 870, 3393, 7598, 13485, 21054, 30305, 41238, 53853, 68150, 84129, 101790, 121133, 142158, 164865, 189254, 215325, 243078, 272513, 303630, 336429, 370910, 407073, 444918, 484445, 525654, 568545, 613118, 659373, 707310, 756929, 808230, 861213
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OFFSET
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0,1
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COMMENTS
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The identity (58*n^2+1)^2-(841*n^2+29)*(2*n)^2 = 1 can be written as A158666(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.: -29*(1+27*x+30*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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29(29Range[0, 40]^2+1) (* or *) LinearRecurrence[{3, -3, 1}, {29, 870, 3393}, 40] (* From Harvey P. Dale, Nov 05 2011 *)
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PROG
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(MAGMA) I:=[29, 870, 3393]; [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=0, 40, print1(841*n^2 + 29", ")); \\ Vincenzo Librandi, Feb 17 2012
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CROSSREFS
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Cf. A158666, A005843.
Sequence in context: A049667 A042626 A157877 * A167738 A107964 A096699
Adjacent sequences: A158662 A158663 A158664 * A158666 A158667 A158668
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 24 2009
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EXTENSIONS
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Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
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STATUS
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approved
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