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A202155
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x-values in the solution to x^2 - 13*y^2 = -1.
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3
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18, 23382, 30349818, 39394040382, 51133434066018, 66371158023650982, 86149711981264908618, 111822259780523827735182, 145145207045407947135357618, 188398366922679734857866452982, 244540935120431250437563520613018, 317413945387952840388222591889244382
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OFFSET
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1,1
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COMMENTS
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The corresponding values of y of this Pell equation are in A202156.
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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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FORMULA
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G.f.: 18*x*(1+x)/(1-1298*x+x^2).
a(n) = -a(-n+1) = (r^(2n-1)-1/r^(2n-1))/2, where r=18+5*sqrt(13).
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MATHEMATICA
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LinearRecurrence[{1298, -1}, {18, 23382}, 12]
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PROG
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(Magma) m:=13; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(18*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), n, 1, 12);
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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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STATUS
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approved
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