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%I #41 May 24 2021 16:33:34
%S 1,4,20,304,6784,407684,39072966,9449433606,3830070645700,
%T 3762885306351756,6402694828334379856,25695884677997378383120
%N a(n) is the number of tilings of the order-n Aztec Diamond by square tetrominoes and Z-shaped tetrominoes, counting all rotations and reflections as distinct.
%C Computed by _Don Reble_, Mar 31 2021; a(8) from Mike Beeler, Mar 31 2021; a(9) from Walter Trump, Apr 01 2021
%C Comments from _Allan C. Wechsler_, Mar 31 2021: (Start)
%C Motivated by a query from James Propp in the Math-Fun forum, Mar 28 2021.
%C An Aztec Diamond of order n is a set of squares whose centers are at distance n or closer to a vertex in the taxicab metric.
%C Tilings by dominoes are counted by A006125. (End)
%H James Propp, <a href="https://www.jstor.org/stable/2691169">A Pedestrian Approach to a Method of Conway, or, A Tale of Two Cities</a>, Mathematics Magazine, Vol. 70, No. 5 (Dec., 1997), 327-340.
%Y Cf. A006125.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Mar 31 2021
%E a(10) from _Andrew Howroyd_, Apr 01 2021
%E a(11) from _Walter Trump_, Apr 06 2021
%E a(12) from _Bert Dobbelaere_, May 21 2021