[seqfan] Re: Square forest

[Jeffrey Shallit]

This concept has certainly been studied, under the name "visible lattice 
points" (use a Google scholar search to find lots of papers), but 
mathematicians choose to compute the points in an nxn grid that are 
visible from the origin, and not the slightly strange location you chose...

On 2021-05-22 11:44 a.m., John Mason wrote:
> Hi Seqfans,
> I was surprised not to see this sequence in the database; maybe someone will recognise the idea and point to something similar.
> 
> A forest of trees has been planted on a square grid pattern, n rows by n columns. Each row is separated from the next by one metre, and the same for the columns.
> An observer stands in the middle of one side, exactly one metre outside the forest.
> How many trees trunks can the observe see? Assume that the trunks are very thin, and that any trunk obscures the vision only of other trunks that are perfectly behind it, from the point of view of the observer.
> 
> I calculated the following values: 1, 4, 7, 14, 17, 30, 33, 52, 51, 82, 81, 108, 105, 156, 143, 198, 183, 252, 231, 308, 267, 380, 339, 436, 383, 526, 461, 598, 525, 680.
> For example, if the forest contains 5 by 5 trees, the observer will see only 17, as 8 will be hidden.
> The sequence does not seem to be present, and neither is its “opposite”, the number of hidden trees: 0, 0, 2, 2, 8, 6, 16, 12, 30, 18, 40, 36, 64, 40.
> I tried searching alternate values too, but to no avail.
> I don’t know if there is a formula that will predict a(n); I used simple geometry to find the hidden trees.
> 
> john
> 
> Sent from Mail for Windows 10
> 
> 
>