After n months, assuming no rabbit dies, the newborn pair when n=0 will have produced 1 pair (children) when n=1, 2 pairs when n=2, and so on, so the number of pairs they will produce is n. The firstborn pair will produce n-1 new pairs (grandchildren of the original pair). The second born pair will produce n-2 pairs, etc. (great grandchildren of the original pair). If we sum all these we get n+n-1+n-2+...+2+1=(n+1)(n/2) pairs to which 1 has to be added to account for the initial pair. So the number of pairs P(n) after n months is (n+1)(n/2)+1.
EXAMPLE
n=3 months.
The newborns born on month 0 will breed 3 pairs of children on months 1, 2 and 3.
The children born on month 1 will breed 2 pairs on months 2 and 3—the grandchildren.
The grandchildren born on month 2 will breed 1 pair on month 3—the great grandchildren.
So 7 pairs will exist, including the original pair: 3 pairs of children, 2 pairs of grandchildren and one pair of great grandchildren.