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

1, 2, 5, 22, 94, 524, 3031, 18770, 118133, 758381, 4915652, 32149296, 211637205, 1401194463, 9321454604, 62272330564, 417546684096

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 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.

Wikipedia, Pseudo-polyomino

Example

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

Crossrefs

Cf. A006770.

10th row of A366766.

Sequence in context: A144934 A346628 A371609 * A362790 A369830 A056840

Adjacent sequences: A030219 A030220 A030221 * A030223 A030224 A030225

Keyword

nonn,hard,nice,more

Author

Matthew Cook

Extensions

Computed by Matthew Cook; extended by David W. Wilson

More terms from Joseph Myers, Sep 26 2002

Status

approved