The function f is defined by f(n) = f(n − 1) + f(n − 2). It is also true that f(1) = 3 and f(3) = 10. What is the value of f(6)

It's some problem I came up with and wanted to test people. Answer if you know. I just want to say all of you are smart, and if you don't know, that's okay

This can be done by brute force.

f(3) = f(2) + f(1)

10 = f(2) + 3

f(2) = 7

f(4) = f(3) + f(2)

f(4) = 7 + 10 = 17

f(5) = f(4) + f(3)

f(5) = 17 + 10 = 27

f(6) = f(5) + f(4) = 27 + 17 = 44.

Challenge problem: Find the explicit form of f(n).