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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
OFFSET
0,2
COMMENTS
Used to form integer solutions of Pell equation a^2 - 82*b^2 =-1. See A097738 with A097739.
LINKS
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved