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A097725 Chebyshev U(n,x) polynomial evaluated at x=51. 3
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

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).

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

Adjacent sequences:  A097722 A097723 A097724 * A097726 A097727 A097728

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 August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)