A174559 Triangle T(n,k)of the coefficients [x^(n-k)] of the polynomials q(0,x)=-1, q(1,x)=3*x, q(n,x)=x*q(n-1,x)-q(n-2,x) in row n,column k. A companion to A193002(n).

-1, 3, 0, 3, 0, 1, 3, 0, -2, 0, 3, 0, -5, 0, -1, 3, 0, -8, 0, 1, 0, 3, 0, -11, 0, 6, 0, 1, 3, 0, -14, 0, 14, 0, 0, 0, 3, 0, -17, 0, 25, 0, -6, 0, -1, 3, 0, -20, 0, 39, 0, -20, 0, -1, 0, 3, 0, -23, 0, 56, 0, -45, 0, 5, 0, 1

Offset: 0

Author

Paul Curtz, Aug 20 2011

Keywords

• sign
• tabl

Comments

a(n)=

-1, :-1,

3, 0, :3*x,

3, 0, 1, :3*x^2+1,

3, 0, -2, 0, :3*x^3-2*x,

3, 0, -5, 0, -1,

3, 0, -8, 0, 1, 0

3, 0, -11, 0, 6, 0, 1.

Row sum=period 6:repeat -1, 3, 4, 1, -3, 4=-A117378(n)=A117378(n+3).

Crossrefs

Cf. A192011.

Formula

a(n) + A193002(n)=4*A192174(n).

a(n) - A193002(n)=2*A053119(n), Chebyshev's S(n,x).