A226981 Number of ways to cut an n X n square into squares with integer sides, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 8 elements.

0, 0, 0, 1, 45, 1194, 55777, 4471175, 669049507, 187616301623, 98793450008033, 97702667035688951

Offset: 1

Author

Christopher Hunt Gribble, Jun 25 2013

Keywords

• nonn
• more

Examples

			For n=5, there are 45 dissections where the orbits under the symmetry group of the square, D4, have 8 elements.
For n=4, this is the only dissection:
---------
|   | | |
|   -----
|   |   |
-----   |
| | |   |
---------
| | | | |
---------
		

Links

• Christopher Hunt Gribble, C++ program for A226978, A226979, A226980, A226981, A227004
• Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420

Crossrefs

Cf. A045846, A034295, A219924, A224239, A226978, A226979, A226980.

Formula

A226978(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).

1*A226978(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).

Extensions

a(8)-a(12) from Ed Wynn, Apr 02 2014