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%I #38 Nov 05 2023 09:00:50
%S 1,2,5,22,94,524,3031,18770,118133,758381,4915652,32149296,211637205,
%T 1401194463,9321454604,62272330564,417546684096
%N Number of n-polyplets (polyominoes connected at edges or corners); may contain holes.
%C See A056840 for illustrations, valid also for this sequence up to n=4, but slightly misleading for polyplets with holes. See the colored areas in the illustration of A056840(5)=99 which correspond to identical 5-polyplets. (The 2+2+4-3 = 5 additional figures counted there correspond to the 4-square configuration with a hole inside ({2,4,6,8} on a numeric keyboard), with one additional square added in three inequivalent places: "inside" one angle (touching two sides), attached to one side, and attached to a corner. These do only count for 3 here, but for 8 in A056840.) It can be seen that A056840 counts a sort of "spanning trees" instead, i.e., simply connected graphs that connect all of the vertices (using only "King's moves", and maybe other additional constraints). - _M. F. Hasler_, Sep 29 2014
%H M. F. Hasler, <a href="/A030222/a030222.gif">Illustration of A030222(5)=94 through a colored version of Vicher's image for A056840(5)=99</a>. (Figures filled with same color do not count as different here.)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyplet.html">Polyplet</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pseudo-polyomino">Pseudo-polyomino</a>
%e XXX..XX...XX..X.X..X.. (the 5 for n=3)
%e .......X...X...X....X.
%e .....................X
%Y Cf. A006770.
%Y 10th row of A366766.
%K nonn,hard,nice,more
%O 1,2
%A _Matthew Cook_
%E Computed by _Matthew Cook_; extended by _David W. Wilson_
%E More terms from _Joseph Myers_, Sep 26 2002
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