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A098260
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Chebyshev polynomials S(n,627).
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2
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1, 627, 393128, 246490629, 154549231255, 96902121506256, 60757475635191257, 38094840321143411883, 23885404123881284059384, 14976110290833243961821885, 9389997266948320082778262511
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OFFSET
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0,2
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COMMENTS
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Used for all positive integer solutions of Pell equation x^2 - 629*y^2 = -4. See A098261 with A098262.
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LINKS
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Table of n, a(n) for n=0..10.
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (627, -1).
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FORMULA
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a(n)= S(n, 627)=U(n, 627/2)= S(2*n+1, sqrt(629))/sqrt(629) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x).
a(n)=627*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=627; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (627+25*sqrt(629))/2 and am := (627-25*sqrt(629))/2 = 1/ap.
G.f.: 1/(1-627*x+x^2).
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MATHEMATICA
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LinearRecurrence[{627, -1}, {1, 627}, 20] (* Harvey P. Dale, Aug 28 2012 *)
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CROSSREFS
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Sequence in context: A031703 A158382 A188362 * A224603 A261708 A098261
Adjacent sequences: A098257 A098258 A098259 * A098261 A098262 A098263
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Sep 10 2004
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STATUS
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approved
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