Digital filters with a Fibonacci-based impulse response

The impulse response h(n1, n2) of the all-pole two-dimensional recursive digital filter whose transfer function is H(z, z) = 1/ 1 - a10z1^-1-a01z2^-1-a20z1^-1is shown to be determined everywhere by the response h(n1, 0) along the z1-axis. When a10= 1 = a20, h(n1, 0) is the n1th number in the Fibonacci sequence 1, 1, 2, 3, ..., fk= fk-1+ fk-2,.... This particular example suggests a class of all-pole digital filters which similarly have a Fibonacci-based impulse response characteristic.