A351159 Number of polyominoes of n cells with both diagonal symmetries, for which the 180-degree rotational symmetry has an axis that coincides with the center of a square, but without 90-degree rotational symmetry.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 3, 1, 6, 4, 9, 6, 20, 19, 32, 25, 64, 82, 114, 107, 217, 332, 397, 442, 751, 1316, 1400, 1787, 2632, 5194, 4973, 7179, 9349, 20344, 17810, 28676, 33557, 79675, 64309, 114122, 121511, 311733, 233891, 453183, 443271, 1220628, 856220, 1797275, 1627497, 4782790, 3152912, 7122490, 6009640, 18760227, 11671571, 28214840, 22303296, 73658526, 43411073, 111753108

Offset

1,11

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056878.

Links

Table of n, a(n) for n=1..66.

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

Formula

For odd n, a(n) = A056878(n); for even n, a(n) = A056878(n) - A351160(n/2).

a(n) = (A390653(n) - 4*A351615(n) - 2*A351190(n) - 2*A351142(n) - A351127(n))/2. - John Mason, Nov 14 2025

Example

For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common.

Crossrefs

Cf. A000105, A056878, A351160, A390653, A351615, A351190, A351142, A351127.

Sequence in context: A205858 A340793 A053222 * A318762 A391191 A262598

Adjacent sequences: A351156 A351157 A351158 * A351160 A351161 A351162

Keyword

nonn

Author

John Mason, Feb 03 2022

Extensions

a(33)-a(50), using data from Toshihiro Shirakawa, John Mason, Nov 14 2025

Corrected from a(44) and extended to a(66) by John Mason, Dec 09 2025

Status

approved