%I #21 Jul 08 2024 10:38:06
%S 1,68,65536,1073758208,281474976710656,1180591620734591172608,
%T 79228162514264337593543950336,85070591730234615870455337876369440768,
%U 1461501637330902918203684832716283019655932542976,401734511064747568885490523085607563280607805796072384626688
%N The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is not fixed under any of these symmetries.
%H Peter Kagey, <a href="/A367529/a367529.pdf">Illustration of a(2)=68</a>
%H Peter Kagey and William Keehn, <a href="https://arxiv.org/abs/2311.13072">Counting tilings of the n X m grid, cylinder, and torus</a>, arXiv: 2311.13072 [math.CO], 2023. See also <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Kagey/kagey6.html">J. Int. Seq.</a>, (2024) Vol. 27, Art. No. 24.6.1, pp. A-6, A-9.
%F a(2m-1) = 256^(m^2 - m).
%F a(2m) = 1/4 (16^m^2 + 256^m^2).
%t Table[{256^(m^2 - m), 1/4*(16^m^2 + 256^m^2)}, {m, 1, 5}] // Flatten
%Y Cf. A367525, A367526, A367527, A367528.
%K nonn
%O 1,2
%A _Peter Kagey_, Dec 10 2023