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A030222 Number of n-polyplets (polyominoes connected at edges or corners); may contain holes. 20
1, 2, 5, 22, 94, 524, 3031, 18770, 118133, 758381, 4915652, 32149296, 211637205, 1401194463, 9321454604, 62272330564, 417546684096 (list; graph; refs; listen; history; text; internal format)
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
M. F. Hasler, Illustration of A030222(5)=94 through a colored version of Vicher's image for A056840(5)=99. (Figures filled with same color do not count as different here.)
Eric Weisstein's World of Mathematics, Polyplet.
Wikipedia, Pseudo-polyomino
XXX..XX...XX..X.X..X.. (the 5 for n=3)
Cf. A006770.
10th row of A366766.
Sequence in context: A144934 A346628 A371609 * A362790 A369830 A056840
Computed by Matthew Cook; extended by David W. Wilson
More terms from Joseph Myers, Sep 26 2002

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)