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%I #12 Dec 21 2023 11:05:05
%S 1,2,3,4,10,4,8,36,32,10,16,136,256,136,16,32,528,2048,2080,512,36,64,
%T 2080,16384,32896,16384,2080,64,128,8256,131072,524800,524288,131328,
%U 8192,136,256,32896,1048576,8390656,16777216,8390656,1048576,32896,256
%N Table read by antidiagonals downward: T(n,k) is the number of tilings of the n X k grid up to horizontal reflection by an asymmetric tile.
%H Peter Kagey, <a href="/A368222/a368222.pdf">Illustration of T(3,2)=32</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.
%e Table begins:
%e n\k| 1 2 3 4 5 6
%e ---+---------------------------------------------
%e 1 | 1 2 4 8 16 32
%e 2 | 3 10 36 136 528 2080
%e 3 | 4 32 256 2048 16384 131072
%e 4 | 10 136 2080 32896 524800 8390656
%e 5 | 16 512 16384 524288 16777216 536870912
%e 6 | 36 2080 131328 8390656 536887296 34359869440
%t A368222[n_, m_] := 2^(n*m/2 - 1) (2^(n*m/2) + Boole[EvenQ[n]])
%Y Cf. A368220, A368221, A368224, A117401.
%K nonn,tabl
%O 1,2
%A _Peter Kagey_, Dec 18 2023
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