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A097740 Chebyshev U(n,x) polynomial evaluated at x=201. 2
1, 402, 161603, 64964004, 26115368005, 10498312974006, 4220295700182407, 1696548373160353608, 682008225714761968009, 274165610188961150786010, 110213893287736667854008011, 44305710936059951516160434412 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

Used to form integer solutions of Pell equation a^2 - 101*b^2 =-1. See A097741 with A097742.

LINKS

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n) = 2*201*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.

a(n) = S(n, 2*201)= U(n, 201), Chebyshev's polynomials of the second kind. See A049310.

G.f.: 1/(1-402*x+x^2).

a(n)= sum((-1)^k*binomial(n-k, k)*402^(n-2*k), k=0..floor(n/2)), n>=0.

a(n) = ((201+20*sqrt(101))^(n+1) - (201-20*sqrt(101))^(n+1))/(40*sqrt(101)), n>=0.

CROSSREFS

Sequence in context: A104391 A158312 A128767 * A083815 A165808 A097741

Adjacent sequences:  A097737 A097738 A097739 * A097741 A097742 A097743

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 15 21:56 EST 2012. Contains 205860 sequences.