cp's OEIS Frontend

A367526 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by two tiles that are each fixed under both of these reflections.

%I A367526 #24 Jul 06 2024 10:19:52
%S A367526 2,9,168,16960,8407040,17180983296,140737630961664,
%T A367526 4611686053860868096,604462909825456529211392,
%U A367526 316912650057075646247661993984,664613997892457973921852429862699008,5575186299632655785536225887234636434636800,187072209578355573530072906199130068813267662274560
%N A367526 The number of ways of tiling the n X n grid up to diagonal and antidiagonal reflections by two tiles that are each fixed under both of these reflections.
%H A367526 Peter Kagey, <a href="/A367526/a367526_2.pdf">Illustration of a(2)=9</a>
%H A367526 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 A367526 a(2m-1) = 2^(2m^2 - 4m - 1)(4^m + 4^m^2 + 8^m).
%F A367526 a(2m)   = 4^(m^2 - 1)(1 + 2^(1 + m) + 4^m^2).
%t A367526 Table[{2^(2 m^2 - 4 m - 1) (4^m + 4^m^2 + 8^m), 4^(m^2 - 1) (1 + 2^(1 + m) + 4^m^2)}, {m, 1, 5}] // Flatten
%Y A367526 Cf. A054247, A367526, A367527, A367528, A367529.
%K A367526 nonn
%O A367526 1,1
%A A367526 _Peter Kagey_, Dec 10 2023