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A202156
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y-values in the solution to x^2 - 13*y^2 = -1.
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3
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5, 6485, 8417525, 10925940965, 14181862955045, 18408047189707445, 23893631070377308565, 31013914721302556809925, 40256037414619648361974085, 52252305550261582271285552405, 67823452348202119168480285047605, 88034788895660800419105138706238885
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OFFSET
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1,1
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COMMENTS
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The corresponding values of x of this Pell equation are in A202155.
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, Dover (New York), 1966, p. 264.
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 1..200
Tanya Khovanova, Recursive Sequences.
A. M. S. Ramasamy, Polynomial solutions for the Pell's equation, Indian Journal of Pure and Applied Mathematics 25 (1994), p. 579 (Theorem 4, case t=1).
J. P. Robertson, Solving the generalized Pell equation x^2-D*y^2=N, pp. 9, 24.
Index entries for linear recurrences with constant coefficients, signature (1298,-1).
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FORMULA
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G.f.: 5*x*(1-x)/(1-1298*x+x^2).
a(n) = a(-n+1) = 5*(r^(2n-1)+1/r^(2n-1))/(r+1/r), where r=18+5*sqrt(13).
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MATHEMATICA
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LinearRecurrence[{1298, -1}, {5, 6485}, 12]
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PROG
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(MAGMA) m:=13; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(5*x*(1-x)/(1-1298*x+x^2)));
(Maxima) makelist(expand(((18+5*sqrt(13))^(2*n-1)-(18-5*sqrt(13))^(2*n-1))/(2*sqrt(13))), n, 1, 12);
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CROSSREFS
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Cf. A002313, A003654, A031396, A075871, A202155.
Sequence in context: A079812 A137694 A292334 * A117711 A203689 A116140
Adjacent sequences: A202153 A202154 A202155 * A202157 A202158 A202159
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Dec 15 2011
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STATUS
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approved
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