[seqfan] Re: Parking lot for bad drivers

[Frank Adams-Watters]

Can we show that limit a(n)/n^2 = 1/3? This follows from the conjectured formula, but it might be easier to prove than that.

Franklin T. Adams-Watters

-----Original Message-----
From: Rob Pratt <Rob.Pratt at sas.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Jul 17, 2015 2:57 pm
Subject: [seqfan] Re: Parking lot for bad drivers


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-----Original
Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
Bob Selcoe
Sent: Thursday, July 16, 2015 2:34 AM
To: Sequence Fanatics
Discussion list
Subject: [seqfan] Re: Parking lot for bad drivers

Hi Rob &
Seqfans,

Would you please provide a solution for A260090(15) = 85?  I can
only see 84 as maximum.

Thanks,
Bob
Selcoe


--------------------------------------------------
From: "Rob
Pratt" <Rob.Pratt at sas.com>
Sent: Wednesday, July 15, 2015 3:41 PM
To:
"Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan]
Re: Parking lot for bad drivers

> At Neil's request, I created a new entry
(will be 
> http://oeis.org/A260090).  I described it in terms of attacking
kings 
> on a chessboard and conjectured a formula.
>
> -----Original
Message-----
> From: Rob Pratt
> Sent: Wednesday, July 15, 2015 11:29 AM
>
To: Sequence Fanatics Discussion list
> Subject: RE: [seqfan] Re: Parking lot
for bad drivers
>
> And here’s a less trivial 26-car solution:
>
>
XX_XX_XX
> ________
> XX_XX_XX
> ________
> XX_XX_X_
> _______X
>
X_X_X___
> X_X_X_XX
>
> For n in 1,...,8, I get the following, which is not
in OEIS:
> 1, 2, 4, 8, 12, 16, 21, 26
>
> -----Original Message-----
> From:
SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of 
> APPLEGATE, DAVID
L (DAVID L)
> Sent: Wednesday, July 15, 2015 10:54 AM
> To: Sequence Fanatics
Discussion list
> Subject: [seqfan] Re: Parking lot for bad drivers
>
> I
wonder if I misunderstand the problem as well - as I understand the 
> problem,
there's a trivial 24-car solution for the 8x8 lot:
>
> XX_XX_XX
> ________
>
XX_XX_XX
> ________
> XX_XX_XX
> ________
> XX_XX_XX
> ________
>
> David
Applegate
>
> -----Original Message-----
> From: SeqFan
[mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Rob 
> Pratt
> Sent:
Wednesday, July 15, 2015 10:45 AM
> To: Sequence Fanatics Discussion list
>
Subject: [seqfan] Re: Parking lot for bad drivers
>
> Sorry, I just realized
that I misinterpreted your problem to mean no 
> three in a row, so A181018
provides only an upper bound.
>
> -----Original Message-----
> From: Rob
Pratt
> Sent: Wednesday, July 15, 2015 10:42 AM
> To: 'Sequence Fanatics
Discussion list'
> Subject: RE: [seqfan] Parking lot for bad drivers
>
>
https://oeis.org/A181018
>
> -----Original Message-----
> From: SeqFan
[mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Dale 
> Gerdemann
> Sent:
Wednesday, July 15, 2015 6:22 AM
> To: Sequence Fanatics Discussion list
>
Subject: [seqfan] Parking lot for bad drivers
>
> Hello seqfans,
>
> Here's
a puzzle from p. 39 of "Let's be Less Stupid" by Patricia Marx:
>
> At the
parking lot for bad drivers, you are not allowed to park in a 
> spot that is
next to two occupied spots. In other words, no three cars 
> can be
contiguous--vertically, horizontally, or diagonally. ... How 
> many cars can
the lot fit.
>
> As an example, the book shows an 8x8 "parking lot" (looks
like a
> chessboard) and gives a solution fitting 16 cars into this lot.
>
>
Is this in the OEIS?
>
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