Given the following sequence
$u_0=1$;
$u_1=1$;
$u_n=u_{n-1} + u_{\lfloor n/2\rfloor} + u_{\lfloor n/2\rfloor-5}$
($u_n=0$ for every $n<0$)
I would like to find a closed form for this sequence. I googled a lot and I found several methods and tutorials about finding the closed form (e.g. for Fibonacci, linear recurrence relations), but none of them mention what to do if you have terms like $u_{\lfloor n/2\rfloor}$ in your relations. Does the closed form exist in this case? How to solve it? Thank you in advance!