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 A097765 Chebyshev U(n,x) polynomial evaluated at x=243=2*11^2+1. 2
 1, 486, 236195, 114790284, 55787841829, 27112776338610, 13176753512722631, 6403875094406860056, 3112270119128221264585, 1512556874021221127728254, 735099528504194339854666859, 357256858296164427948240365220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 122*b^2 =-1. See A097766 with A097767. LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (486, -1). FORMULA a(n) = 2*243*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*243)= U(n, 243), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-486*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*486^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((243+22*sqrt(122))^(n+1) - (243-22*sqrt(122))^(n+1))/(44*sqrt(122)), n>=0. MATHEMATICA LinearRecurrence[{486, -1}, {1, 486}, 12] (* Ray Chandler, Aug 12 2015 *) CROSSREFS Sequence in context: A206146 A128969 A223412 * A179428 A252076 A178813 Adjacent sequences:  A097762 A097763 A097764 * A097766 A097767 A097768 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified August 21 09:54 EDT 2017. Contains 290864 sequences.