A174169 A generalized Chebyshev transform of the Motzkin numbers A001006.

1, 1, -1, -2, 0, 0, -3, 1, 8, 1, 1, 26, 7, -51, -3, 0, -264, -186, 348, -120, -285, 2697, 2871, -2304, 3393, 8029, -25795, -36872, 16108, -60010, -159683, 213795, 413712, -181857, 833779, 2669534, -1272977, -4030235, 3611168, -9145271, -39467427

Offset: 0

Author

Paul Barry, Mar 10 2010

Keywords

• easy
• sign

Comments

Hankel transform is the (1,3) Somos-4 sequence A174170.

Formula

G.f.: (1-x+3x^2-sqrt(1-2x+3x^2-6x^3+9x^4))/(2x^2)=(1/(1+3x))*M(x/(1+3x^2)), M(x) the g.f. of A010006;

a(n) = sum{k=0..floor(n/2), (-3)^k*A001006(n-2k)}.

Conjecture: (n+2)*a(n) -(2*n+1)*a(n-1) +3*(n-1)*a(n-2) +3*(5-2*n)*a(n-3) +9*(n-4)*a(n-4)=0. - R. J. Mathar, Sep 30 2012