A174559 - OEIS

%I #15 Mar 30 2012 18:52:05

%S -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,

%T -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,

%U -23,0,56,0,-45,0,5,0,1

%N 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).

%C a(n)=

%C -1,   :-1,

%C 3,  0,   :3*x,

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

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

%C 3,  0,  -5,  0, -1,

%C 3,  0,  -8,  0,  1, 0

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

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

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

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

%Y Cf. A192011.

%K sign,tabl

%O 0,2

%A _Paul Curtz_, Aug 20 2011