A226981 - OEIS

%I #20 Apr 05 2014 13:25:34

%S 0,0,0,1,45,1194,55777,4471175,669049507,187616301623,98793450008033,

%T 97702667035688951

%N 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.

%H Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>

%H Ed Wynn, <a href="http://arxiv.org/abs/1308.5420">Exhaustive generation of Mrs Perkins's quilt square dissections for low orders</a>, arXiv:1308.5420

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

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

%e For n=5, there are 45 dissections where the orbits under the symmetry group of the square, D4, have 8 elements.

%e For n=4, this is the only dissection:

%e ---------

%e |   | | |

%e |   -----

%e |   |   |

%e -----   |

%e | | |   |

%e ---------

%e | | | | |

%e ---------

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

%K nonn,more

%O 1,5

%A _Christopher Hunt Gribble_, Jun 25 2013

%E a(8)-a(12) from _Ed Wynn_, Apr 02 2014