## $F(m) = F(m-2\sqrt{m}+2) + F(m-3\sqrt{m}+2)$ [closed]

$F(m) = F(m-2\sqrt{m}+2) + F(m-3\sqrt{m}+2)$

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why would you think there would be a closed-form solution to this? – Will Sawin Oct 6 2011 at 1:20
Could you include some more background about where this functional equation comes from? – Yemon Choi Oct 6 2011 at 1:24
1. this can be transformed to be a sub-series of fibonacci series, hence it is promissing to find out one closed-form solution. 2. this function is the number of nodes of one un-balanced search tree – John Oct 6 2011 at 1:36
What does the formula mean when $m$ is not a square? – Yemon Choi Oct 6 2011 at 2:01
@John: What is $m$? – Steve Richards Oct 6 2011 at 2:16