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A030222 Number of n-polyplets (polyominoes connected at edges or corners); may contain holes. 8
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)
OFFSET

1,2

COMMENTS

See A056840 for illustrations, valid also for this sequence up to n=4, but slightly misleading for polyplets with holes. See the coloured 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

LINKS

Table of n, a(n) for n=1..17.

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.

EXAMPLE

XXX..XX...XX..X.X..X.. (the 5 for n=3)

.......X...X...X....X.

.....................X

CROSSREFS

Cf. A006770.

Sequence in context: A083465 A215100 A144934 * A056840 A241345 A126797

Adjacent sequences:  A030219 A030220 A030221 * A030223 A030224 A030225

KEYWORD

nonn,hard,nice

AUTHOR

Matthew Cook

EXTENSIONS

Computed by Matthew Cook; extended by David W. Wilson

More terms from Joseph Myers, Sep 26 2002

STATUS

approved

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Last modified October 23 16:07 EDT 2014. Contains 248468 sequences.