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A228209
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x-values in the solutions to x^2 - 10y^2 = 9.
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3
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3, 7, 13, 57, 253, 487, 2163, 9607, 18493, 82137, 364813, 702247, 3119043, 13853287, 26666893, 118441497, 526060093, 1012639687, 4497657843, 19976430247, 38453641213, 170792556537, 758578289293, 1460225726407, 6485619490563, 28805998562887, 55450123962253
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: -x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3) / (x^6-38*x^3+1).
a(n) = 38*a(n-3)-a(n-6).
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MATHEMATICA
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CoefficientList[Series[-(7 x^6 + 13 x^5 + 57 x^4 - 13 x^3 - 7 x^2 - 3 x) / (x^6 - 38 x^3 + 1), {x, 1, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{0, 0, 38, 0, 0, -1}, {3, 7, 13, 57, 253, 487}, 30] (* Harvey P. Dale, Jan 06 2014 *)
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PROG
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(PARI) Vec(-x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3)/(x^6-38*x^3+1) + O(x^100))
(Magma) I:=[3, 7, 13, 57, 253, 487]; [n le 6 select I[n] else 38*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Aug 17 2013 *)
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CROSSREFS
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KEYWORD
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nonn,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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