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A097737
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Chebyshev U(n,x) polynomial evaluated at x=163.
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3
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1, 326, 106275, 34645324, 11294269349, 3681897162450, 1200287180689351, 391289939007565976, 127559319829285818825, 41583946974408169370974, 13556239154337233929118699, 4419292380366963852723324900
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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 - 82*b^2 =-1. See A097738 with A097739.
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LINKS
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FORMULA
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a(n) = 2*163*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*163)= U(n, 163), Chebyshev's polynomials of the second kind. See A049310.
a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0.
a(n)= sum((-1)^k*binomial(n-k, k)*326^(n-2*k), k=0..floor(n/2)), n>=0.
G.f.: 1/(1-326*x+x^2).
a(n) = ((163+18*sqrt(82))^(n+1) - (163-18*sqrt(82))^(n+1))/(36*sqrt(82)), n>=0.
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MATHEMATICA
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LinearRecurrence[{326, -1}, {1, 326}, 12] (* 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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STATUS
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approved
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