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A098248 Chebyshev polynomials S(n,291). 3

%I #12 Feb 09 2017 09:16:12

%S 1,291,84680,24641589,7170617719,2086625114640,607200737742521,

%T 176693328057958971,51417151264128318040,14962214324533282590669,

%U 4353952951287921105566639,1266985346610460508437301280

%N Chebyshev polynomials S(n,291).

%C Used for all positive integer solutions of Pell equation x^2 - 293*y^2 = -4. See A098249 with A098250.

%H Indranil Ghosh, <a href="/A098248/b098248.txt">Table of n, a(n) for n = 0..405</a>

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

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (291,-1).

%F 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).

%F a(n)=291*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=291; a(-1):=0.

%F 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.

%F G.f.: 1/(1-291*x+x^2).

%t LinearRecurrence[{291,-1},{1,291},20] (* _Harvey P. Dale_, Dec 27 2015 *)

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 10 2004

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)