A097725 Chebyshev U(n,x) polynomial evaluated at x=51.
1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612, 1266901427852682470066413, 129211523844680701491725514, 13178308530729578869685936015
Offset: 0
Links
- 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).
Programs
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Mathematica
ChebyshevU[Range[0,20],51] (* Harvey P. Dale, Oct 08 2012 *) LinearRecurrence[{102, -1},{1, 102},15] (* Ray Chandler, Aug 11 2015 *)
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)).
Extensions
More terms from Harvey P. Dale, Oct 08 2012
Comments