Consider the following polynomial in 2 variables with 9 a(n) coefficients:
I generate the following table based on the points to be interpolated, x and y can each have values [-1,0,1], and the sum x+y is related to the range of the function. So x=-1 y=-1 x+y = -2, from the list of points the value of the function at -2 is 3 so A is three there.
I haven't tried but I imagine wider ranges with more variables would work as well. I also suppose you could narrow the thickness of the band by ranging one variable over a smaller interval like y from -.5...5 and x from -1.5..1.5