A390653 a(n) is the number of n-celled fixed polyominoes with at least 180 degree rotational symmetry about the center of a square in the lattice.

1, 0, 2, 0, 7, 0, 24, 1, 86, 6, 316, 27, 1178, 114, 4442, 472, 16896, 1926, 64716, 7789, 249283, 31348, 964708, 125802, 3748031, 503948, 14610484, 2016677, 57118440, 8065830, 223859532, 32251819, 879285686, 128955260, 3460424846, 515657653, 13642112667, 2062335114, 53865266960, 8250061654, 212982833863, 33011955188

Offset

1,3

Comments

Column R180C of the Shirakawa link.

Links

John Mason, Table of n, a(n) for n = 1..59

Toshihiro Shirakawa, Enumeration of Polyominoes up to Size N=59, arXiv:2510.22446 [math.CO], 2025. See p. 5-6.

Formula

a(n) = 4*A351615(n) + 2*A351190(n) + 2*A351159(n) + 2*A351142(n) + A351127(n).

Crossrefs

Cf. A001168, A351615, A351190, A351159, A351142, A351127, A390654, A390655.

Sequence in context: A266220 A022897 A192496 * A156442 A268683 A174968

Adjacent sequences: A390650 A390651 A390652 * A390654 A390655 A390656

Keyword

nonn

Author

John Mason, Nov 14 2025

Status

approved