

A030222


Number of npolyplets (polyominoes connected at edges or corners); may contain holes.


11



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 colored areas in the illustration of A056840(5)=99 which correspond to identical 5polyplets. (The 2+2+43 = 5 additional figures counted there correspond to the 4square 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: A215100 A307155 A144934 * A056840 A321608 A241345
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



