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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used to form integer solutions of Pell equation a^2 - 37*b^2 =-1. See A097729 with A097730.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..461

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 (146, -1)

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

Adjacent sequences:  A097725 A097726 A097727 * A097729 A097730 A097731

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.