what sequences most need extending?

[Richard Guy]

Perhaps not completely relevant, but there's
quite a bit of literature on packing unit
squares in squares.  See D4 in UPIG.  For
example, 5 unit squares can be packed in a
square of edge  2 + root(2)/2.     R.

On Thu, 26 May 2005, Franklin T. Adams-Watters wrote:

> Following the links, I see that this is intended to be restricted to the packings with the squares aligned with the sides of the rectangle.  Since it isn't clear that this is always the smallest rectangle that the squares can be fit into, I think the description should indicate this - unless somebody can prove that the best result is always with the squares aligned to the rectangle - in which case, the comments should indicate that.
>
> Ed Pegg Jr <edp at wolfram.com> wrote:
>> ID Number: A081287
>> URL:       http://www.research.att.com/projects/OEIS?Anum=A081287
>> Sequence:  0,1,1,5,5,8,14,6,15,20,7,17,17,20,25,16,9,30,21,20,33
>> Name:      Excess area when consecutive squares of size 1 to n are
>> packed into the smallest possible rectangle.
> --
> Franklin T. Adams-Watters
> 16 W. Michigan Ave.
> Palatine, IL 60067
> 847-776-7645
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