A226979 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 2 elements.

0, 0, 0, 2, 2, 24, 36, 344, 504, 7657, 11978, 289829

Offset

1,4

Links

Table of n, a(n) for n=1..12.

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

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).

A226979(n) = A240120(n) + A240121(n) + A240122(n).

Example

For n=5, there are 2 dissections where the orbits under the symmetry group of the square, D4, have 2 elements.
For n=4, the 2 dissections can be seen in A240120 and A240121.

Crossrefs

Cf. A045846, A034295, A219924, A224239, A226978, A226980, A226981, A240120, A240121, A240122.

Sequence in context: A279311 A248812 A226243 * A261517 A131448 A156447

Adjacent sequences: A226976 A226977 A226978 * A226980 A226981 A226982

Keyword

nonn,more

Author

Christopher Hunt Gribble, Jun 25 2013

Extensions

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

Status

approved