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A097725 Chebyshev U(n,x) polynomial evaluated at x=51. 2
1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612 (list; graph; refs; listen; history; 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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

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)).

CROSSREFS

Sequence in context: A163435 A203401 A030512 * A129751 A094095 A187882

Adjacent sequences:  A097722 A097723 A097724 * A097726 A097727 A097728

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004

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Last modified February 17 12:23 EST 2012. Contains 206011 sequences.