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%I #13 Dec 21 2023 11:05:23
%S 1,6,6,16,76,16,72,1056,1056,72,256,16576,65536,16576,256,1056,262656,
%T 4196352,4196352,262656,1056,4096,4197376,268435456,1073790976,
%U 268435456,4197376,4096,16512,67117056,17180000256,274878431232,274878431232,17180000256,67117056,16512
%N Table read by antidiagonals: T(n,k) is the number of tilings of the n X k grid up to horizontal and vertical reflections by an asymmetric tile.
%H Peter Kagey, <a href="/A368220/a368220.pdf">Illustration of T(2,2)=76</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
%e ----+-----------------------------------------------------------
%e 1 | 1 6 16 72 256
%e 2 | 6 76 1056 16576 262656
%e 3 | 16 1056 65536 4196352 268435456
%e 4 | 72 16576 4196352 1073790976 274878431232
%e 5 | 256 262656 268435456 274878431232 281474976710656
%e 6 | 1056 4197376 17180000256 70368756760576 288230376688582656
%t A368220[n_, m_] := 2^(n*m - 2)*(2^(n*m) + Boole[EvenQ[n*m]] + Boole[EvenQ[n]] + Boole[EvenQ[m]])
%Y Cf. A117401, A225910, A368218, A368219, A368222, A368224.
%K nonn,tabl
%O 1,2
%A _Peter Kagey_, Dec 18 2023
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