cp's OEIS Frontend

A368220 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.

%I A368220 #17 Jul 09 2024 08:56:34
%S A368220 1,6,6,16,76,16,72,1056,1056,72,256,16576,65536,16576,256,1056,262656,
%T A368220 4196352,4196352,262656,1056,4096,4197376,268435456,1073790976,
%U A368220 268435456,4197376,4096,16512,67117056,17180000256,274878431232,274878431232,17180000256,67117056,16512
%N A368220 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 A368220 Peter Kagey, <a href="/A368220/a368220.pdf">Illustration of T(2,2)=76</a>
%H A368220 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-1, A-3.
%e A368220 Table begins:
%e A368220   n\k |    1       2           3              4                  5
%e A368220   ----+-----------------------------------------------------------
%e A368220     1 |    1       6          16             72                256
%e A368220     2 |    6      76        1056          16576             262656
%e A368220     3 |   16    1056       65536        4196352          268435456
%e A368220     4 |   72   16576     4196352     1073790976       274878431232
%e A368220     5 |  256  262656   268435456   274878431232    281474976710656
%e A368220     6 | 1056 4197376 17180000256 70368756760576 288230376688582656
%t A368220 A368220[n_, m_] := 2^(n*m - 2)*(2^(n*m) + Boole[EvenQ[n*m]] + Boole[EvenQ[n]] + Boole[EvenQ[m]])
%Y A368220 Cf. A117401, A225910, A368218, A368219, A368222, A368224.
%K A368220 nonn,tabl
%O A368220 1,2
%A A368220 _Peter Kagey_, Dec 18 2023