combinatorics

I hope this is the right place. Sorry, if it isn't. Thank you for previous.

But I can't figure this out;

There be one pair of newborn butterflies during the first month and the butterflies will become adults in a month. the an adult pair will give birth to a new pair of butterflies after a month continuing the increase in the moon once, one time in month.
How many pair of butterflies will be about during the n month?

- is it 1 * something until n month? How you calculate this?

This exercise is more-commonly posed using rabbits. :wink:

Ah, I see. Thanks for telling!, I didn't know that this is a famous and big thing.
But in this butterfly/rabbit case; is it like this;

1 month =1
2 month = 2
3 month = 3
4 month = 5
5 month = 8
6 month = 13
7 month =21 pairs. ?

if this goes like this, what about n month?