

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.


5



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

1,5


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).


EXAMPLE

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:

   
 
  
 
   

    



CROSSREFS

Cf. A045846, A034295, A219924, A224239, A226978, A226979, A226980.
Sequence in context: A320822 A229796 A143400 * A173000 A004350 A199518
Adjacent sequences: A226978 A226979 A226980 * A226982 A226983 A226984


KEYWORD

nonn,more


AUTHOR

Christopher Hunt Gribble, Jun 25 2013


EXTENSIONS

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


STATUS

approved



