# [seqfan] Re: Parking lot for bad drivers

Bob Selcoe rselcoe at entouchonline.net
Sat Jul 18 00:35:43 CEST 2015

```I have also proposed an equivalent conjecture for n >= 5: a(n) = a(n-1) +
n - A103469(n-2).   That may also aid in a proof.

Cheers,
Bob

--------------------------------------------------
From: "Frank Adams-Watters" <franktaw at netscape.net>
Sent: Friday, July 17, 2015 5:20 PM
To: <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Parking lot for bad drivers

> 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
>
>
> XX_XX_XX_XX_X_X
> ____________X_X
> XX_X_X_X_XX____
> ___X_X_X____X_X
> XX_______XX_X_X
> ___XX_XX_______
> XX_______X_X_XX
> ___X_X_X_X_X___
> XX_X_X_______XX
> _______XX_XX___
> X_X_XX_______XX
> X_X____X_X_X___
> ____XX_X_X_X_XX
> X_X____________
> X_X_XX_XX_XX_XX
>
> -----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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```