Digital filters with a Fibonacci-based impulse response

The impulse response h(n
1
, n
2
) of the all-pole two-dimensional recursive digital filter whose transfer function is H(z, z) = 1/ 1 - a
10
z
1
^-1
-a
01
z
2
^-1
-a
20
z
1
^-1
is shown to be determined everywhere by the response h(n
1
, 0) along the z
1
-axis. When a
10
= 1 = a
20
, h(n
1
, 0) is the n
1
th number in the Fibonacci sequence 1, 1, 2, 3, ..., f
k
= f
k-1
+ f
k-2
,.... This particular example suggests a class of all-pole digital filters which similarly have a Fibonacci-based impulse response characteristic.