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A098263
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Chebyshev polynomials S(n,731).
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2
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1, 731, 534360, 390616429, 285540075239, 208729404383280, 152580909064102441, 111536435796454501091, 81532981986299176195080, 59600498295548901344102389, 43567882721064260583362651279
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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 - 733*y^2 = -4. See A098291 with A098292.
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LINKS
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FORMULA
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a(n)= S(n, 731)=U(n, 731/2)= S(2*n+1, sqrt(733))/sqrt(733) 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)=731*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=731; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (731+27*sqrt(733))/2 and am := (731-27*sqrt(733))/2 = 1/ap.
G.f.: 1/(1-731*x+x^2).
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MATHEMATICA
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LinearRecurrence[{731, -1}, {1, 731}, 20] (* Harvey P. Dale, Jun 21 2020 *)
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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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