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A097765 Chebyshev U(n,x) polynomial evaluated at x=243=2*11^2+1. 2


%S 1,486,236195,114790284,55787841829,27112776338610,13176753512722631,

%T 6403875094406860056,3112270119128221264585,1512556874021221127728254,

%U 735099528504194339854666859,357256858296164427948240365220

%N Chebyshev U(n,x) polynomial evaluated at x=243=2*11^2+1.

%C Used to form integer solutions of Pell equation a^2 - 122*b^2 =-1. See A097766 with A097767.

%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 (486, -1).

%F a(n) = 2*243*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.

%F a(n) = S(n, 2*243)= U(n, 243), Chebyshev's polynomials of the second kind. See A049310.

%F G.f.: 1/(1-486*x+x^2).

%F a(n)= sum((-1)^k*binomial(n-k, k)*486^(n-2*k), k=0..floor(n/2)), n>=0.

%F a(n) = ((243+22*sqrt(122))^(n+1) - (243-22*sqrt(122))^(n+1))/(44*sqrt(122)), n>=0.

%t LinearRecurrence[{486, -1},{1, 486},12] (* _Ray Chandler_, Aug 12 2015 *)

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 31 2004

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Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)