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A097774
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Chebyshev U(n,x) polynomial evaluated at x=393=2*14^2+1.
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2
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1, 786, 617795, 485586084, 381670044229, 299992169177910, 235793463303793031, 185333362164612144456, 145671786867921841749385, 114497839144824403002872154, 89995155896045112838415763659
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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 - 197*b^2 =-1. See A097775 with A097776.
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LINKS
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FORMULA
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a(n) = 2*393*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*393)= U(n, 393), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-2*393*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*786^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((393+28*sqrt(197))^(n+1) - (393-28*sqrt(197))^(n+1))/(56*sqrt(197)), n>=0.
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MATHEMATICA
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LinearRecurrence[{786, -1}, {1, 786}, 30] (* or *) CoefficientList[ Series[ 1/(1-786x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jun 15 2011 *)
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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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