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A097728 Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1. 1
1, 146, 21315, 3111844, 454307909, 66325842870, 9683118751111, 1413669011819336, 206385992606871945, 30130941251591484634, 4398911036739749884619, 642210880422751891669740 (list; graph; refs; listen; history; 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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

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)).

CROSSREFS

Sequence in context: A183654 A183653 A166219 * A172877 A172911 A172933

Adjacent sequences:  A097725 A097726 A097727 * A097729 A097730 A097731

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.