Determine the pattern: What comes next?

. 1,1,2,4,7,_
.4,9,16,25,_

Explain. I do not get the patterns. Please help me. Thank you.

1 + 0 = 1

1 + 1 = 2
2 + 2 = 4

Now do you see that pattern?

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4 + 5 = 9
9 + 7 = 16

Take it from there.