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%I #26 Jul 06 2024 10:19:56
%S 1,7,144,16704,8396800,17180459008,140737555464192,
%T 4611686036680998912,604462909816110680375296,
%U 316912650057066639048407252992,664613997892457954898647603849723904,5575186299632655785460668023508722111217664,187072209578355573530072277557703869206096815063040
%N The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by a tile that is fixed under diagonal reflection, but not antidiagonal reflection.
%H Peter Kagey, <a href="/A367527/a367527_1.pdf">Illustration of a(2)=7</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) = 2^(2m^2 - 4m - 2)*(2^(1 + 2 m^2) + 8^m).
%F a(2m) = 4^(m^2 - 1)*(1 + 2^m + 4^m^2).
%t Table[{2^(2 m^2 - 4 m - 2) (2^(1 + 2 m^2) + 8^m), 4^(m^2 - 1) (1 + 2^m + 4^m^2)}, {m, 1, 5}] // Flatten
%Y Cf. A302484, A367526, A367528, A367529.
%K nonn
%O 1,2
%A _Peter Kagey_, Dec 10 2023