[seqfan] Re: How many ways to dissect a square into 4 congruent pieces

[Giovanni Resta]

On 05/12/2015 07:21 PM, Neil Sloane wrote:
> ....
> See A003213. Many it is time someone found the next term!

I tried.

I followed the same approach described by Parkin and I
recomputed the terms from a(1) to a(5), plus the new ones a(6) and a(7).

What I got is
1, 5, 37, 766, 43318, 7695805, 4015896016, where

Parkin got
1, 5, 37, 782, 44240.

There is a discrepancy in a(4) and a(5).

I tried to understand where the discrepancy arose by
looking at the last page of the Parkin paper scanned in A003213.

Parking reported separate counts for the dissection of the
squares (2n)X(2n) in 4 pieces with rotational symmetry
and for the dissection of the rectangles nX(2n) in two pieces.

For the rectangles I got the same results as Parkin.

For the squares I got the same results except when
the starting point of the path from the border to the
center is on the midpoint of the border.

In particular, I obtain the same results reported in A064941 and
this increases a little my confidence (usually very low...).

It would be nice if somebody could check at least the
case a(4) = 766 or 782, so to understand who is right and
which one between A003213 and A064941 has to be corrected.

Giovanni