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

Author

Matthew Cook

Keywords

• nonn
• hard
• nice
• more

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

Examples

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

Links

• 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

Crossrefs

Cf. A006770.

10th row of A366766.

Extensions

Computed by Matthew Cook; extended by David W. Wilson

More terms from Joseph Myers, Sep 26 2002