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Sep 9, 2021 at 13:41 comment added Tony Huynh I agree. I basically did the minimal amount of work to show that the ratio (if it exists) is strictly less than $\frac{1}{2}$, but the answer is not too illuminating. Would be nice if there were a more conceptual answer.
Sep 9, 2021 at 13:04 comment added Sam Hopkins This is nice, but it is ultimately pretty similar to the full linear recurrence, compute the asymptotic growth rate approach.
Sep 9, 2021 at 12:06 history edited Tony Huynh CC BY-SA 4.0
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Sep 9, 2021 at 9:47 history edited Tony Huynh CC BY-SA 4.0
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Sep 9, 2021 at 8:02 history edited Tony Huynh CC BY-SA 4.0
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Sep 9, 2021 at 7:58 history edited YCor CC BY-SA 4.0
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Sep 9, 2021 at 7:24 history answered Tony Huynh CC BY-SA 4.0