cp's OEIS Frontend

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

%I A030222 #39 Feb 16 2025 08:32:35
%S A030222 1,2,5,22,94,524,3031,18770,118133,758381,4915652,32149296,211637205,
%T A030222 1401194463,9321454604,62272330564,417546684096
%N A030222 Number of n-polyplets (polyominoes connected at edges or corners); may contain holes.
%C A030222 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
%H A030222 M. F. Hasler, <a href="/A030222/a030222.gif">Illustration of A030222(5)=94 through a colored version of Vicher's image for A056840(5)=99</a>. (Figures filled with same color do not count as different here.)
%H A030222 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polyplet.html">Polyplet</a>.
%H A030222 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pseudo-polyomino">Pseudo-polyomino</a>
%e A030222 XXX..XX...XX..X.X..X.. (the 5 for n=3)
%e A030222 .......X...X...X....X.
%e A030222 .....................X
%Y A030222 Cf. A006770.
%Y A030222 10th row of A366766.
%K A030222 nonn,hard,nice,more
%O A030222 1,2
%A A030222 _Matthew Cook_
%E A030222 Computed by _Matthew Cook_; extended by _David W. Wilson_
%E A030222 More terms from _Joseph Myers_, Sep 26 2002