A097740 Chebyshev U(n,x) polynomial evaluated at x=201.

1, 402, 161603, 64964004, 26115368005, 10498312974006, 4220295700182407, 1696548373160353608, 682008225714761968009, 274165610188961150786010, 110213893287736667854008011, 44305710936059951516160434412

Offset

0,2

Comments

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

Links

Indranil Ghosh, Table of n, a(n) for n = 0..383

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 (402, -1).

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.

Mathematica

LinearRecurrence[{402, -1}, {1, 402}, 12] (* Ray Chandler, Aug 11 2015 *)

Crossrefs

Sequence in context: A158312 A237177 A128767 * A325151 A213605 A083815

Adjacent sequences: A097737 A097738 A097739 * A097741 A097742 A097743

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 31 2004

Status

approved