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A097728
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Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1.
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2
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1, 146, 21315, 3111844, 454307909, 66325842870, 9683118751111, 1413669011819336, 206385992606871945, 30130941251591484634, 4398911036739749884619, 642210880422751891669740
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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 - 37*b^2 =-1. See A097729 with A097730.
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LINKS
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FORMULA
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a(n) = 2*73*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*73)= U(n, 73), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-146*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*146^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((73+12*sqrt(37))^(n+1) - (73-12*sqrt(37))^(n+1))/(24*sqrt(37)).
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MATHEMATICA
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LinearRecurrence[{146, -1}, {1, 146}, 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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