A194084 Triangle read by rows: a(n)=A135929(n) + A192011(n). Row n gives coefficients of polynomials BC(n,x) in order of decreasing exponents.

0, 3, 0, 3, 0, 3, 3, 0, 0, 0, 3, 0, -3, 0, -3, 3, 0, -6, 0, -3, 0, 3, 0, -9, 0, 0, 0, 3, 3, 0, -12, 0, 6, 0, 6, 0, 3, 0, -15, 0, 15, 0, 6, 0, -3, 3, 0, -18, 0, 27, 0, 0, 0, -9, 0

Offset

0,2

Comments

0,

3, 0,

3, 0, 3,

3, 0, 0, 0,

3, 0, -3, 0, -3,

3, 0, -6, 0, -3, 0.

Multiples of 3.

Row sum (from the second) is period 6: 3*A057079(n),"from" A057083 (scaled Chebyshev U(n,x)).

If a(0)=-3, a(n)=3*A192174(n).

Links

Table of n, a(n) for n=0..54.

Formula

BC(0,x)=0, BC(1,x)=3*x, BC(2,x)=3*x^2+3, BC(n,x)=x*BC(n-1,x) - BC(n-2,x), n > 2.

Example

a(0)=1-1=0, a(1)=1+2=3, a(2)=0+0=0.

Crossrefs

Sequence in context: A307199 A141030 A221168 * A262281 A297871 A292130

Adjacent sequences: A194081 A194082 A194083 * A194085 A194086 A194087

Keyword

sign,tabl

Author

Paul Curtz, Aug 14 2011

Status

approved