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%I #25 Apr 16 2023 09:22:49
%S 1,1,4,10,34,110,388,1369,4982,18246,67727,253014,952275,3602743,
%T 13698525,52297602,200402285,770414503,2970385477,11482405741,
%U 44491816601,172766346508,672186393972,2619994613794,10228901862928,39996339056273,156612019296546,614044339256951
%N Number of poly-IH68-tiles (holes allowed) with n cells.
%C Equivalently, polyominoes where two polyominoes are considered the same if and only if they are related by a translation or a reflection in a NE-SW diagonal line.
%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 6.2 and 9.4.
%H John Mason, <a href="/A182645/b182645.txt">Table of n, a(n) for n = 1..50</a>
%H Jean-François Alcover, <a href="/A182645/a182645.txt">Mathematica program</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%F a(n) = 4*A006749(n) + 2*A006746(n) + 3*A006748(n) + 2*A006747(n) + A056877(n) + 2*A056878(n) + A144553(n) + A142886(n). - _Andrew Howroyd_, Dec 04 2018
%Y Polyominoes by group of symmetries relating shapes considered the same: A000105 (all symmetries), A001168 (translations only), A000988 (rotations and translations), A056780 (horizontal and vertical reflections, rotations of order 2 and translations), A056783 (reflections in either diagonal, rotations of order 2 and translations), A151522 (rotations of order 2 and translations), A151525 (reflections in a horizontal line and translations), A182645 (reflections in a NE-SW diagonal line and translations)
%K nonn
%O 1,3
%A _Joseph Myers_, Nov 24 2010
%E a(19)-a(28) from _Andrew Howroyd_, Dec 04 2018
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