[seqfan] Re: Packing many different square sizes in a square

[Giovanni Resta]

On 06/18/2013 06:31 PM, Allan Wechsler wrote:

> Up to n=16, the answer seems to be ceiling(n/2), but I cannot pack 9
> different square sizes on a 17x17 board.  The sequence I have so far is
>
> 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,8,9,9,9
>
> and if this is right, it's not in OEIS yet. Can any sequence fanatic
> increase any of these numbers?  Or give more terms?

I got these terms, for n=1,..,33.

1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 
10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14

I've attached the packing for n=33 which so far is the most "dense"
one, in the sense that the ratio between number of unit squares and 
total area is the smallest.

Giovanni