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A041527
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Denominators of continued fraction convergents to sqrt(280).
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2
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1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530, 246481, 254011, 754503, 1008514, 2771531, 3780045, 123732971, 127513016, 378759003, 506272019, 1391303041, 1897575060, 62113704961, 64011280021, 190136265003, 254147545024, 698431355051, 952578900075
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,502,0,0,0,0,0,-1).
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FORMULA
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a(0)=1, a(1)=1, a(2)=3, a(3)=4, a(4)=11, a(5)=15, a(6)=491, a(7)=506, a(8)=1503, a(9)=2009, a(10)=5521, a(11)=7530, a(n)=502*a(n-6)-a(n-12). - Harvey P. Dale, Aug 13 2012
G.f.: -(x^2-x-1)*(x^8+4*x^6+15*x^4+4*x^2+1) / (x^12-502*x^6+1). - Colin Barker, Nov 18 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[280], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 502, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530}, 30] (* Harvey P. Dale, Aug 13 2012 *)
CoefficientList[Series[-(x^2 - x - 1) (x^8 + 4 x^6 + 15 x^4 + 4 x^2 + 1)/(x^12 - 502 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)
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PROG
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(Magma) I:=[1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530]; [n le 12 select I[n] else 502*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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