Daily Challenge #65- A Disguised Sequence

Given u0 = 1, u1 = 2 and the relation 6unun+1-5unun+2+un+1un+2 = 0 calculate un for any integer n >= 0.

Example:
fcn(n) returns un: fcn(17) -> 131072, fcn(21) -> 2097152

Note:
You can look at this as

-Purely algorithmic from the definition of u^n
-the second one - not at all mandatory, but as a compliment - is to get a bit your head around and find which sequence is hidden behind u^n

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This challenge comes from g964 at CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

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Comments

[bb4L]

for others not understanding the task, check out the link to the original: codewars.com/kata/563f0c54a22b9345...

$6u_n u_{n+1} - 5 u_n u_{n+2} + u_{n+1} u_{n+2}= 0$

[thirteenturtles]

I didn't understand the recurrence relation. Is 6unun == 6*un*un?