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A030222
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Number of n-polyplets (polyominoes connected at edges or corners); may contain holes.
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20
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1, 2, 5, 22, 94, 524, 3031, 18770, 118133, 758381, 4915652, 32149296, 211637205, 1401194463, 9321454604, 62272330564, 417546684096
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Eric Weisstein's World of Mathematics, Polyplet.
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EXAMPLE
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XXX..XX...XX..X.X..X.. (the 5 for n=3)
.......X...X...X....X.
.....................X
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CROSSREFS
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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_Matthew Cook_
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EXTENSIONS
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Computed by _Matthew Cook_; extended by _David W. Wilson_
More terms from _Joseph Myers_, Sep 26 2002
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STATUS
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approved
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