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A097844 Chebyshev polynomials S(n,171). 4


%S 1,171,29240,4999869,854948359,146191169520,24997835039561,

%T 4274483600595411,730911697866775720,124981625851618052709,

%U 21371127108928820237519,3654337754000976642563040,624870384807058077058042321,106849181464252930200282673851

%N Chebyshev polynomials S(n,171).

%C Used for all positive integer solutions of Pell equation x^2 - 173*y^2 = -4. See A097845 with A098244.

%H Indranil Ghosh, <a href="/A097844/b097844.txt">Table of n, a(n) for n = 0..446</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 (171, -1).

%F a(n)= S(n, 171)=U(n, 171/2)= S(2*n+1, sqrt(173))/sqrt(173) 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)=171*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=171; a(-1):=0.

%F a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (171+13*sqrt(173))/2 and am := (171-13*sqrt(173))/2 = 1/ap.

%F G.f.: 1/(1-171*x+x^2).

%t CoefficientList[Series[1/(1-171x+x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {171,-1},{1,171},30] (* _Harvey P. Dale_, Mar 21 2013 *)

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 10 2004

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Last modified December 14 17:37 EST 2018. Contains 318103 sequences. (Running on oeis4.)