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A097725
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Chebyshev U(n,x) polynomial evaluated at x=51.
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3
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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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Indranil Ghosh, Table of n, a(n) for n = 0..496
Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
R. Flórez, R. A. Higuita, and A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (102,-1).
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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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ChebyshevU[Range[0, 20], 51] (* Harvey P. Dale, Oct 08 2012 *)
LinearRecurrence[{102, -1}, {1, 102}, 15] (* Ray Chandler, Aug 11 2015 *)
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CROSSREFS
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Sequence in context: A274252 A303993 A030512 * A353142 A129751 A225993
Adjacent sequences: A097722 A097723 A097724 * A097726 A097727 A097728
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Aug 31 2004
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EXTENSIONS
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More terms from Harvey P. Dale, Oct 08 2012
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STATUS
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approved
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