A226980 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 4 elements.

0, 0, 1, 6, 26, 264, 1157, 23460, 153485, 6748424, 70521609, 6791578258

Offset: 1

Author

Christopher Hunt Gribble, Jun 25 2013

Keywords

• nonn
• more

Examples

			For n=5, there are 26 dissections where the orbits under the symmetry group of the square, D4, have 4 elements.
The 6 dissections for n=4 can be seen in A240123 and A240125.
		

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, A226981, A240123, A240124, A240125.

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).

A226980(n) = A240123(n) + A240124(n) + A240125(n).

Extensions

a(8)-a(12) from Ed Wynn, Apr 01 2014