This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367523 #25 Jul 06 2024 10:03:31
%S A367523 1,4,70,8292,4195360,8590033024,70368748374016,2305843010824323072,
%T A367523 302231454903932172107776,158456325028529097399561355264,
%U A367523 332306998946228968514182141758668800,2787593149816327892693735671512138485071872,93536104789177786765035834129545391718695404830720
%N A367523 The number of ways of tiling the n X n grid up to the symmetries of the square by a tile that is fixed under 90-degree rotations, but not reflections.
%H A367523 Peter Kagey, <a href="/A367523/a367523.pdf">Illustration of a(3)=70</a>
%H A367523 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-7.
%F A367523 a(2m-1) = 2^(m^2 - 4m - 2)*(2^(3m+1) + 2^(m^2+2m) + 8^m^2).
%F A367523 a(2m) = 2^(m^2 - 3)*(2 + 3*2^m^2 + 8^m^2) = A367522(2m).
%t A367523 Table[{2^(-2 + (-4 + n) n) (2^(n (2 + n)) + 2^(1 + 3 n) + 8^n^2), 2^(-3 + n^2) (2 + 3 2^n^2 + 8^n^2)}, {n, 1, 5}] // Flatten
%Y A367523 Cf. A054247, A295229, A302484, A367522, A367524, A367525.
%K A367523 nonn
%O A367523 1,2
%A A367523 _Peter Kagey_, Dec 10 2023