A193002 -id:A193002 - cp's OEIS frontend

A174559 Triangle T(n,k)of the coefficients [x^(n-k)] of the polynomials q(0,x)=-1, q(1,x)=3x, q(n,x)=xq(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

Graph
List
Refs
Listen
History
Text
Internal format

Paul Curtz, Aug 20 2011

sign
tabl

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).

Cf. A192011.

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Crossrefs

Formula

cp's OEIS Frontend

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).

Views

Author

Keywords

Comments

Crossrefs

Formula

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