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There was a question trying to find a closed form solution for,

$$F(n)=\sum_i^n \lfloor i/5 \rfloor$$

I got that for $n$ in the range $[5 \cdot k-6,5 \cdot k-1]$, where $k$ is a positive natural number, the solution is,

$$F_{[5 \cdot k-6,5 \cdot k-1]}(n)=k \cdot n-{1 \over 2} \cdot (7 \cdot k-5 \cdot k^2)$$

Where the subscript limits the domain of $F$. I don't really care about posting the answer, I'd just like the Op of the question to know the solution. If it helps, I believe Thomas Andrews had a partial answer. Ideally, I'd like this information to be passed on to the Op.

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    $\begingroup$ Your browser's history might help. $\endgroup$ – user147263 Sep 8 '15 at 2:17
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    $\begingroup$ If it's the question Antonio found, I also have something to be passed on to the OP, and it isn't information. What a piece of work! $\endgroup$ – Gerry Myerson Sep 8 '15 at 5:47
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    $\begingroup$ What an attitude! Do we really want that reopened? I need to commute now, so cannot send in a warning, but, rest assured, one is coming. $\endgroup$ – Jyrki Lahtonen Sep 8 '15 at 6:09
  • $\begingroup$ This is a new user who apparently has several misunderstandings about how the site works. I addressed a few in a ModMessage. Other moderators may chime in with theirs. Sigh, if only the new users would spend a little while learning the site norms. $\endgroup$ – Jyrki Lahtonen Sep 8 '15 at 9:23
  • $\begingroup$ @JyrkiLahtonen I agree. Would you mind directing the Op to this page, if (s)he is interested in an answer? $\endgroup$ – Zach466920 Sep 8 '15 at 14:05
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    $\begingroup$ Don't overlook the option of posting the question you want to answer as a new question. $\endgroup$ – Hurkyl Sep 8 '15 at 14:30
  • $\begingroup$ @Hurkyl Thanks for the suggestion, I'll try doing that when I have a bit of time. $\endgroup$ – Zach466920 Sep 8 '15 at 14:45
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This question (viewable to users with 10k+ rep) by user268254 asked about a recurrence of the form

$$ F(n) = \sum_{i=0}^{n} F\left(\left\lfloor\frac{i}{5}\right\rfloor\right), $$

and it does have a (deleted) partial answer by Thomas Andrews. Perhaps this is the question you were thinking of, though it doesn't seem directly related to your sum.

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  • $\begingroup$ At the moment, users below 10k can view (some version of) this question in Google Cache. Try to search for "1424411/evaluating-a-recurrence-in-faster-than-on". I will also add link directly to Google cache (although I am not sure whether such links are stable: webcache.googleusercontent.com/… $\endgroup$ – Martin Sleziak Sep 8 '15 at 6:20
  • $\begingroup$ Thanks. As far as my answer is concerned, each $k$ only gives a solution in a certain range. For instance, for $k=2$ it gives a solution if $4 \le n \le 9$, and $n$ is an integer. $\endgroup$ – Zach466920 Sep 8 '15 at 14:04

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