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 A097731 Chebyshev U(n,x) polynomial evaluated at x=99 = 2*7^2+1. 5
 1, 198, 39203, 7761996, 1536836005, 304285766994, 60247045028807, 11928610629936792, 2361804657682456009, 467625393610496352990, 92587466130220595436011, 18331850668390067399977188 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 50*b^2 =-1. See A097732 with A097733. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..434 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 linear recurrences with constant coefficients, signature (198, -1). FORMULA a(n) = 2*99*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*99)= U(n, 99), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-198*x+x^2). a(n) = sum((-1)^k*binomial(n-k, k)*198^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((99+70*sqrt(2))^(n+1) - (99-70*sqrt(2))^(n+1))/(140*sqrt(2)), n>=0. a(n) = Pell(6*n + 6)/Pell(6). Sum_{n >= 0} 1/( 14*a(n) + 1/(14*a(n)) ) = 1/14. - Peter Bala, Mar 25 2015 MAPLE with (combinat):seq(fibonacci(6*n, 2)/70, n=1..12); # Zerinvary Lajos, Apr 21 2008 MATHEMATICA LinearRecurrence[{198, -1}, {1, 198}, 12] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A278017 A270849 A324454 * A006243 A171391 A151738 Adjacent sequences:  A097728 A097729 A097730 * A097732 A097733 A097734 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified October 19 11:09 EDT 2019. Contains 328216 sequences. (Running on oeis4.)