A226978 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 1 element.

1, 2, 2, 4, 4, 12, 8, 44, 32, 228, 148, 1632, 912, 16004, 8420, 213680, 101508, 3933380, 1691008, 98949060, 38742844, 3413919788, 1213540776, 161410887252, 52106993880

Offset

1,2

Comments

From Walter Trump, Dec 15 2022: (Start)

a(n) is the number of fully symmetric dissections of an n X n square into squares with integer sides.

Conjecture: For n>3 the number of dissections is a multiple of 4. (End)

Links

Table of n, a(n) for n=1..25.

Christopher Hunt Gribble, C++ program for A226978, A226979, A226980, A226981, A227004

Walter Trump, Example for n=19

Formula

a(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).

1*a(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).

Example

For n=5, there are 4 dissections where the orbits under the symmetry group of the square, D4, have 1 element.
For n=4, 3 dissections divide the square into uniform subsquares (of sizes 1, 2 and 4 respectively), and this is the 4th:
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Crossrefs

Cf. A045846, A034295, A219924, A224239, A226979, A226980, A226981.

Sequence in context: A081164 A125553 A218147 * A243331 A300218 A138317

Adjacent sequences: A226975 A226976 A226977 * A226979 A226980 A226981

Keyword

nonn,more

Author

Christopher Hunt Gribble, Jun 25 2013

Extensions

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

a(13)-a(25) from Walter Trump, Dec 15 2022

Status

approved