Padovan rabbits

Recurrence relation
According to Wikipedia, "In mathematics, a recurrence relation is an equation that recursively defines a sequence: each term of the sequence is defined as a function of the preceding terms."

The Padovan recurrence relation can describe the rabbit population if one change is made to the initial conditions. That change would add a condition pertaining to month zero, a condition that isn't considered for the Fibonacci rabbits. Because Padovan requires the terms Tn-2 and Tn-3 in order to find Tn, then the new condition would allow us to generate the sequence past T1 and T2 (which are givens by the initial conditions). In other words, without a new condition, pertaining to month zero, we could not generate the Padovan sequence using the corresponding formula. We would need to use the Fibonacci formula for the first three terms, and from there on use the Padovan formula.

Therefore, by these new conditions:
(*) In month zero, you have one pair of adult (2-month old) rabbits.
(1) You begin with one pair of rabbits which have just been born.
(2) Each rabbit reaches sexual maturity after one month.
(3) The gestation period of a rabbit is one month.
(4) A female rabbit will always give birth to one pair of rabbits.
(5) The life span of a rabbit is three months.

This new condition (*), gives us:
T0 = 1
T1 = 1
T2 = 1
With these conditions, we may now derive the sequence using only the Padovan recurrence relation.