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A098263 Chebyshev polynomials S(n,731). 2
1, 731, 534360, 390616429, 285540075239, 208729404383280, 152580909064102441, 111536435796454501091, 81532981986299176195080, 59600498295548901344102389, 43567882721064260583362651279 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Used for all positive integer solutions of Pell equation x^2 - 733*y^2 = -4. See A098291 with A098292.
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
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).
MATHEMATICA
LinearRecurrence[{731, -1}, {1, 731}, 20] (* Harvey P. Dale, Jun 21 2020 *)
CROSSREFS
Sequence in context: A031525 A031705 A158396 * A289571 A098291 A255798
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 10 2004
STATUS
approved

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Last modified May 19 04:28 EDT 2024. Contains 372666 sequences. (Running on oeis4.)