[seqfan] Re: Square forest

[Allan Wechsler]

If, instead of standing one meter outside the forest near the center of one
side, the observer displaces the corner tree, the resulting sequence is
https://oeis.org/A049691. This, unsurprisingly, is closely related to Farey
series, and provides a bunch of related sequences and references. Some
insight might be had there. In the meantime, I would encourage adding this
one.

On Sat, May 22, 2021 at 11:45 AM John Mason <masonmilan33 at gmail.com> 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
>
>
>
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