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A097728
Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1.
2
1, 146, 21315, 3111844, 454307909, 66325842870, 9683118751111, 1413669011819336, 206385992606871945, 30130941251591484634, 4398911036739749884619, 642210880422751891669740
OFFSET
0,2
COMMENTS
Used to form integer solutions of Pell equation a^2 - 37*b^2 =-1. See A097729 with A097730.
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*73*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*73)= U(n, 73), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-146*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*146^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((73+12*sqrt(37))^(n+1) - (73-12*sqrt(37))^(n+1))/(24*sqrt(37)).
MATHEMATICA
LinearRecurrence[{146, -1}, {1, 146}, 12] (* Ray Chandler, Aug 11 2015 *)
CROSSREFS
Sequence in context: A183653 A231243 A166219 * A172877 A172911 A172933
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved