Smallest polyomino with n holes

[David Wilson]

I can show that p <= 2 n + 2 sqrt(3n+1) + 1 infinitely often, where p is the 
size of the minimal polyomino with n holes.

----- Original Message ----- 
From: <franktaw at netscape.net>
To: <seqfan at ext.jussieu.fr>
Sent: Tuesday, May 23, 2006 9:15 AM
Subject: Smallest polyomino with n holes


> How big is the smallest polyomino with n holes?  According to 
> //www.ieeta.pt/%7Etos/animals/a44.html, the sequence starts:
>
> 7,11,14,17,19,23,25
>
> It seems like there ought to be a significantly faster way to determine 
> this than by enumerating all polyominos and determining the smallest one.
>
> This sequence was not in the OEIS.  I have now submitted it.
>
> Franklin T. Adams-Watters
>
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