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A097725 Chebyshev U(n,x) polynomial evaluated at x=51. 4
1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612, 1266901427852682470066413, 129211523844680701491725514, 13178308530729578869685936015 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Used to form integer solutions of Pell equation a^2 - 26*b^2 =-1. See A097726 with A097727.
LINKS
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
FORMULA
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)).
MATHEMATICA
ChebyshevU[Range[0, 20], 51] (* Harvey P. Dale, Oct 08 2012 *)
LinearRecurrence[{102, -1}, {1, 102}, 15] (* Ray Chandler, Aug 11 2015 *)
CROSSREFS
Sequence in context: A274252 A303993 A030512 * A353142 A129751 A225993
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
EXTENSIONS
More terms from Harvey P. Dale, Oct 08 2012
STATUS
approved

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Last modified July 23 12:38 EDT 2024. Contains 374549 sequences. (Running on oeis4.)