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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
OFFSET
0,2
COMMENTS
Used to form integer solutions of Pell equation a^2 - 122*b^2 =-1. See A097766 with A097767.
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved