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%I #9 Mar 16 2017 14:12:26
%S 1,531,281960,149720229,79501159639,42214966048080,22416067470370841,
%T 11902889611800868491,6320411967798790797880,
%U 3356126852011546112805789,1782097038006163187109076079,946290171054420640808806592160
%N Chebyshev polynomials S(n,531).
%C Used for all positive integer solutions of Pell equation x^2 - 533*y^2 = -4. See A098258 with A098259.
%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 (531, -1).
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F a(n)= S(n, 531)=U(n, 531/2)= S(2*n+1, sqrt(533))/sqrt(533) 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)=531*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=531; a(-1):=0.
%F a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (531+23*sqrt(533))/2 and am := (531-23*sqrt(533))/2 = 1/ap.
%F G.f.: 1/(1-531*x+x^2).
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 10 2004
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