A292065 -id:A292065 - cp's OEIS frontend

A292157 Number of Besźel [Beszel] Polycubes with n cells, identifying mirror images. A Besźel Polycube is a polycube whose cells each have two or more even coordinates.

1, 1, 2, 4, 11, 23, 80, 230, 837, 2935, 11251, 43364, 173205, 699160, 2868527, 11872515, 49583430, 208407805, 881085265

Offset: 1

George Sicherman, Sep 09 2017

This sequence also gives the number of Ul Qoma Polycubes with n cells. An Ul Qoma Polycube is a polycube whose cells each have two or more odd coordinates.

			a(4) = 4 because 4 of the 8 tetracubes (I, L, T, K) can be embedded in the Besźel section of the cubic grid.

China Miéville, The City & the City, Macmillan, 2009.

G. L. Sicherman, Catalogue of Besźel Polycubes

Cf. A292065: Number of Besźel Polycubes with n cells, distinguishing mirror images; A038119: Number of polycubes with n cells, identifying mirror images.

a(11) - a(19) from Joerg Arndt, Dec 12 2023

A294151 Number of perforated polyominoes with n cells, identifying mirror images.

Original entry on oeis.org

1, 1, 2, 3, 8, 13, 36, 76, 202, 482, 1281, 3277, 8749, 23083, 62056, 166498, 450576, 1220542, 3321870, 9057388, 24769906

Offset: 1

George Sicherman, Oct 23 2017

A perforated polyomino is a polyomino in which every cell has at least one even coordinate.

			a(4)=3 because there are 5 tetrominoes, and the skew and square tetrominoes do not lie in the perforated grid, which leaves 3.

Cf. A000105, number of polyominoes with n cells; A292065, number of Besźel Polycubes with n cells, distinguishing mirror images; A292157, same but identifying mirror images.

a(16) - a(21) from Joerg Arndt, Dec 11 2023

cp's OEIS Frontend

A292157 Number of Besźel [Beszel] Polycubes with n cells, identifying mirror images. A Besźel Polycube is a polycube whose cells each have two or more even coordinates.

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