| a(n) = 34*a(n-1)-a(n-2), a(0)=-1, a(1)=1.
a(n+1) = S(2*n, 6)= S(n, 34) + S(n-1, 34), n>=1, with S(n, x) := U(n, x/2) Chebyshev's polynomials of the second kind. See A049310. S(n, 34)=A029547(n).
G.f.: x*(1+x)/(1-34*x+x^2).
a(n+1) = sum((-1)^k*binomial(2*n-k, k)*6^(2*(n-k)), k=0..n), n>=0.
a(n) = A001109(2n+1). - Lekraj Beedassy, Apr 23 2003
Define f[x,s] = s x + Sqrt[(s^2-1)x^2+1]; f[0,s]=0. a(n) = f[f[a(n-1),3],3]. - Marcos Carreira, Dec 27 2006
Contribution from Antonio Alberto Olivares, Mar 22 2008: (Start)
a(n) = (sqrt(2)/8)(3+2*sqrt(2))*(17+12*sqrt(2))^(n-1) -(sqrt(2)/8)(3-2*sqrt(2))*(17-12*sqrt(2))^(n-1).
a(n) = (sqrt(2)/8)*(17+12*sqrt(2))^(n-1/2) -(sqrt(2)/8)*(17-12*sqrt(2))^(n-1/2).
a(n) = (sqrt(2)/8)*(3+2*sqrt(2))^(2n-1) -(sqrt(2)/8)*(3-2*sqrt(2))^(2n-1).
a(n) = (sqrt(2)/8)*(1+sqrt(2))^(4n-2) -(sqrt(2)/8)*(1-sqrt(2))^(4n-2).
a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3). (End)
a(n+1) = 17*a(n)+6*(8*a(n)^2+1)^0.5 for n>=0. - Richard Choulet (richardchoulet(AT)yahoo.fr), May 01 2009
a(n) = b such that (-1)^(n+1) * Integral_{x=-Pi/2..Pi/2} cos((2*n-1)*x)/(3-sin(x)) dx = c + b*ln(2). - Francesco Daddi, Aug 01 2011
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