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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

R. Flórez, R. A. Higuita, 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: A284448 A274252 A030512 * A129751 A225993 A237432

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 May 28 20:12 EDT 2017. Contains 287241 sequences.