Just 1’s and 2’s

In how many ways can you represent a number as a sum of 1’s and 2’s?

Some examples:

Number	Different Ways	Total ways
3	1+1+1, 2+1, 1+2	3
4	1+1+1+1, 2+2, 1+1+2, 2+1+1, 1+2+1	5

Note that sums written in different orders are considered different.

2+1 and 1+2 are considered different combinations.

Submit your answer for the following numbers. How many ways can you write them as a sum of 1’s and 2’s? Do you see a pattern emerge?

5

6

7

Do you see any patterns? Or a strategy you can use to find the number of way?

Can you predict the number of ways for representing 10, without actually counting the cases?

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