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A098263 Chebyshev polynomials S(n,731). 2

%I

%S 1,731,534360,390616429,285540075239,208729404383280,

%T 152580909064102441,111536435796454501091,81532981986299176195080,

%U 59600498295548901344102389,43567882721064260583362651279

%N Chebyshev polynomials S(n,731).

%C Used for all positive integer solutions of Pell equation x^2 - 733*y^2 = -4. See A098291 with A098292.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (731, -1).

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%F 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).

%F a(n)=731*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=731; a(-1):=0.

%F 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.

%F G.f.: 1/(1-731*x+x^2).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 10 2004

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)