Generating Function for Boubaker Polynomials

Theorem
The Boubaker polynomials, defined as:
 * $B_n \left({x}\right) = \begin{cases}

1 & : n = 0 \\ x & : n = 1 \\ x^2+2 & : n = 2 \\ x B_{n-1} \left({x}\right) - B_{n-2} \left({x}\right) & : n > 2 \end{cases}$

have as an ordinary generating function:
 * $\displaystyle f_{B_n, \operatorname{ORD}} \left({x, t}\right) = \sum_{n=0}^{\infty} B_n \left({x}\right) t^n = \frac {1+3t^2} {1+t \left({t-x}\right)}$

Proof
and then solve for $f(x,t)$.