

A324406


Number of oriented polyomino rings of length 4n with fourfold rotational symmetry.


5



1, 1, 1, 2, 4, 8, 16, 33, 67, 141, 295, 630, 1340, 2895, 6237, 13596, 29556, 64846, 141976, 313131, 689425, 1527099, 3377723, 7508724, 16671776, 37175536, 82809462, 185141322, 413555554, 926743719, 2075094083, 4659549155, 10455390287, 23519366120, 52872809784
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OFFSET

1,4


COMMENTS

Redelmeier uses these rings to enumerate polyominoes of the regular tiling {4,4} with fourfold rotational symmetry (A144553) and an even number of cells. Each cell of a polyomino ring is adjacent to (shares an edge with) exactly two other cells. For oriented rings, chiral pairs (though congruent) are counted as two.
For n odd, the center of the ring is a vertex of the tiling; for n even, the center is the center of a tile.


LINKS



FORMULA



EXAMPLE

For a(1)=1, the four cells form a square. For a(2)=1, the eight cells form a 3 X 3 square with the center cell omitted. For a(3)=1, the twelve cells form a 4 X 4 square with the four inner cells omitted. For a(4)=2, the sixteen cells of one ring form a 5 X 5 square with the nine inner cells omitted; the other ring is similar, but with each corner cell omitted and replaced with the cell diagonally toward the center from that corner cell.


CROSSREFS



KEYWORD

nonn,hard


AUTHOR



STATUS

approved



