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A097725
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Chebyshev U(n,x) polynomial evaluated at x=51.
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4
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1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612, 1266901427852682470066413, 129211523844680701491725514, 13178308530729578869685936015
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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 - 26*b^2 =-1. See A097726 with A097727.
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LINKS
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FORMULA
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a(n) = 102*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*51)= U(n, 51), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-102*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*102^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((51+10*sqrt(26))^(n+1) - (51-10*sqrt(26))^(n+1))/(20*sqrt(26)).
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MATHEMATICA
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LinearRecurrence[{102, -1}, {1, 102}, 15] (* Ray Chandler, Aug 11 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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EXTENSIONS
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STATUS
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approved
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