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A097765
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Chebyshev U(n,x) polynomial evaluated at x=243=2*11^2+1.
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2
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1, 486, 236195, 114790284, 55787841829, 27112776338610, 13176753512722631, 6403875094406860056, 3112270119128221264585, 1512556874021221127728254, 735099528504194339854666859, 357256858296164427948240365220
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OFFSET
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0,2
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COMMENTS
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Used to form integer solutions of Pell equation a^2 - 122*b^2 =-1. See A097766 with A097767.
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LINKS
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FORMULA
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a(n) = 2*243*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*243)= U(n, 243), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-486*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*486^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((243+22*sqrt(122))^(n+1) - (243-22*sqrt(122))^(n+1))/(44*sqrt(122)), n>=0.
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MATHEMATICA
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LinearRecurrence[{486, -1}, {1, 486}, 12] (* Ray Chandler, Aug 12 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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