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A097737 Chebyshev U(n,x) polynomial evaluated at x=163. 3
1, 326, 106275, 34645324, 11294269349, 3681897162450, 1200287180689351, 391289939007565976, 127559319829285818825, 41583946974408169370974, 13556239154337233929118699, 4419292380366963852723324900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used to form integer solutions of Pell equation a^2 - 82*b^2 =-1. See A097738 with A097739.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..397

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 (326, -1).

FORMULA

a(n) = 2*163*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.

a(n) = S(n, 2*163)= U(n, 163), Chebyshev's polynomials of the second kind. See A049310.

a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0.

a(n)= sum((-1)^k*binomial(n-k, k)*326^(n-2*k), k=0..floor(n/2)), n>=0.

G.f.: 1/(1-326*x+x^2).

a(n) = ((163+18*sqrt(82))^(n+1) - (163-18*sqrt(82))^(n+1))/(36*sqrt(82)), n>=0.

MATHEMATICA

LinearRecurrence[{326, -1}, {1, 326}, 12] (* Ray Chandler, Aug 11 2015 *)

CROSSREFS

Sequence in context: A138817 A158271 A203723 * A236822 A126311 A097738

Adjacent sequences:  A097734 A097735 A097736 * A097738 A097739 A097740

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified May 28 19:46 EDT 2017. Contains 287241 sequences.