A367525 The number of ways of tiling the n X n grid up to the symmetries of the square by a tile that is not fixed under any of the symmetries of the square.

1, 538, 16777216, 35184378381312, 4722366482869645213696, 40564819207303347603293977182208, 22300745198530623141535718272648361505980416, 784637716923335095479473677930668862955643627524327473152, 1766847064778384329583297500742918515827483896875618958121606201292619776

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Peter Kagey, Illustration of a(2)=538

Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023.

Formula

a(2m-1) = 4096^(m^2 - m).

a(2m) = 8^(m^2 - 1)*(512^m^2 + 3*8^m^2 + 2).

Mathematica

Table[{4096^(m^2 - m), 8^(m^2 - 1) (512^m^2 + 3*8^m^2 + 2)}, {m, 1, 5}] // Flatten

Crossrefs

Cf. A054247, A295229, A302484, A367522, A367523, A367524.

Sequence in context: A252339 A224742 A231194 * A111258 A239347 A118630

Adjacent sequences: A367522 A367523 A367524 * A367526 A367527 A367528

Keyword

nonn

Author

Peter Kagey, Dec 10 2023

Status

approved