I'm embarrassed to report what must be a typical error in my comment "InFibity". I misread the expression a(n -1) = 0 as a(n) - 1 = 0, resulting in a sequence consisting solely of 1's. In turn this suggests an unending or infinite delay before reproduction takes place. Whereas if the delay is zero one would expect the reproduction to be explosively fast, infinitely fast if it takes place in an instant.

So I'd be grateful if anyone could suggest what, if any, sequence is generated by a(n) = a(n-1) + a(n-0) in which the delay is zero. A sequence consisting solely of zeroes? What would that mean?

And what if the delay (D) number were a negative quantity? An anticipation? If D was -1 the sequence generating algorithm would be a(n) = a(n-1) + a(n--1), that is every number is formed by adding the two on either side of it. Given the first two terms 0 1, then we'd get a repetitive sequence going 0 1 1 0 -1 -1 0 1 1 0 -1 -1