

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.


8



0, 0, 1, 6, 26, 264, 1157, 23460, 153485, 6748424, 70521609, 6791578258
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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).
A226980(n) = A240123(n) + A240124(n) + A240125(n).


EXAMPLE

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.


CROSSREFS

Cf. A045846, A034295, A219924, A224239, A226978, A226979, A226981, A240123, A240124, A240125.
Sequence in context: A027283 A009639 A323868 * A199591 A230867 A137088
Adjacent sequences: A226977 A226978 A226979 * A226981 A226982 A226983


KEYWORD

nonn,more


AUTHOR

Christopher Hunt Gribble, Jun 25 2013


EXTENSIONS

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


STATUS

approved



