[seqfan] Re: Parking lot for bad drivers

[M. F. Hasler]

This example shows that a(n) >= (n - floor(n/3)) x (n - floor((n+2)/3))
for this sequence (which is an IMHO more realistic definition of the
parking lot problem, but does not satisfy the initially set condition
of not parking next to two occupied squares)

and thus (I conjecture, at least) a(n) ~ (2n/3)^2 just like A181018.

Maximilian


On Fri, Jul 17, 2015 at 5:39 AM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:
> Sorry, I understood the idea with "movement obliquely"
> by Veikko which beautifully obtained the best result
> of 30 cars. Here is a simpler way namely for BAD drivers
> which also gives 30 cars (with the leaving through the right
> border):
>
>
> XX_XX_XX
> ________
> XX_XX_XX
> XX_XX_XX
> ________
> XX_XX_XX
> XX_XX_XX
> ________
>
>
> Best regards,
> Vladimir
>
>
> ________________________________________
> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
> Sent: 15 July 2015 23:24
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Parking lot for bad drivers
>
> It is important that no car was blocked. For example,
> in Veikko's variant the car a(1,1) is blocked, such that
> even a good driver could not leave, if the leaving is through
> the right border. Then David's variant is the best.
> If the leaving is through either right or downside, then
> the Rob's variant is the best.
> Finally, if to ignore such a requirement (e.g., the leaving is
> through  all borders), then we have 36 cars:
>
> XX_XX_XX
> XX_XX_XX
> ________
> XX_XX_XX
> XX_XX_XX
> ________
> XX_XX_XX
> XX_XX_XX
>
>
>
> Best regards,
> Vladimir
>
> ________________________________________
> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Dale Gerdemann [dale.gerdemann at gmail.com]
> Sent: 15 July 2015 19:58
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Parking lot for bad drivers
>
> The 30 car solution seems to me to conform to Patricia Marx's text.  What
> misinterpretation do you think you made?
>
> I don't know why Marx's solution to her own problem only had 16 cars. Maybe
> she had in mind some unstated conditions or, more likely in my opinion, she
> just didn't work very hard on coming up with an optimal solution.
>
> On Wednesday, July 15, 2015, Veikko Pohjola <veikko at nordem.fi> wrote:
>
>> Ok, seems that I misinterpreted.
>> Sorry
>>
>> Veikko Pohjola kirjoitti 15.7.2015 kello 18.52:
>>
>> > I got 30.
>> >
>> > X_X_X_X_
>> > X______X
>> > _XX_X_X_
>> > XX_XX_XX
>> > ___X_X_X
>> > XX___X__
>> > _X_XX_XX
>> > X___XX__
>> >
>> > Veikko