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A324408 Number of chiral pairs of polyomino rings of length 4n with fourfold rotational symmetry. 3
0, 0, 0, 0, 1, 2, 6, 12, 29, 61, 138, 294, 649, 1402, 3073, 6695, 14676, 32180, 70764, 155849, 344209, 760637, 1687745, 3738854, 8333371, 18496587, 41399110, 92028312, 206765077, 460199821, 1037518525, 2311601665, 5227630580, 11657447790, 26436259384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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. Each chiral ring is congruent to but different from its reflection; the two form a chiral pair.

These chiral rings have fourfold symmetry.

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

Table of n, a(n) for n=1..35.

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

FORMULA

a(n) = A324406(n) - A324407(n) = (A324406(n) - A324409(n)) / 2 = A324407(n) - A324409(n).

EXAMPLE

For a(5) = 1, the pair is   XXX          XXX .

                            X XXX      XXX X

                           XX   X      X   XX

                           X   XX      XX   X

                           XXX X        X XXX

                             XXX        XXX

CROSSREFS

Cf. A324406 (oriented), A324407 (unoriented), A324409 (achiral).

Cf. A144553.

Sequence in context: A057582 A094779 A093387 * A229487 A195166 A225646

Adjacent sequences:  A324405 A324406 A324407 * A324409 A324410 A324411

KEYWORD

nonn,hard

AUTHOR

Robert A. Russell, Feb 26 2019

STATUS

approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)