A226980 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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