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 A098248 Chebyshev polynomials S(n,291). 3
 1, 291, 84680, 24641589, 7170617719, 2086625114640, 607200737742521, 176693328057958971, 51417151264128318040, 14962214324533282590669, 4353952951287921105566639, 1266985346610460508437301280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used for all positive integer solutions of Pell equation x^2 - 293*y^2 = -4. See A098249 with A098250. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..405 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (291,-1). FORMULA a(n)= S(n, 291)=U(n, 291/2)= S(2*n+1, sqrt(293))/sqrt(293) 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)=291*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=291; a(-1):=0. a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (291+17*sqrt(293))/2 and am := (291-17*sqrt(293))/2 = 1/ap. G.f.: 1/(1-291*x+x^2). MATHEMATICA LinearRecurrence[{291, -1}, {1, 291}, 20] (* Harvey P. Dale, Dec 27 2015 *) CROSSREFS Sequence in context: A031695 A158254 A088892 * A185999 A048956 A043439 Adjacent sequences:  A098245 A098246 A098247 * A098249 A098250 A098251 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 10 2004 STATUS approved

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