A292065 -id:A292065

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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.

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..19.

G. L. Sicherman, Catalogue of Besźel Polycubes

EXAMPLE

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

CROSSREFS

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

KEYWORD

nonn,more,hard

AUTHOR

George Sicherman, Sep 09 2017

EXTENSIONS

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

STATUS

approved

A294151

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

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

CROSSREFS

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.