A377155 Number of 3-dimensional polyominoes (or polycubes) with n cells and rotational symmetry group of order exactly 12.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 1, 3, 4, 0, 8, 4, 3, 8, 3, 2, 17, 6, 8, 19, 27, 2, 53, 19, 26, 49, 19, 10, 127, 38, 64, 121, 166, 15, 373, 111, 197, 306, 150, 67, 923, 242, 460, 771, 1100, 115, 2665, 686, 1405, 1972, 1085, 431, 6681, 1562, 3335, 5051, 7353

Offset

1,28

Comments

The sequence counts "one-sided" polycubes (A000162); chiral polycubes count twice.

Links

Table of n, a(n) for n=1..80.

W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.

Formula

a(n) = 2*BD(n)+CCC(n)+DEE(n) = 2*A377128(n)+A377129(n)+A377130(n); see Lunnon paper for naming convention.

Crossrefs

Cf. A000162, A066273, A066281, A066283, A066287, A066288, A066453, A066454, A377128, A377129, A377130.

Sequence in context: A197219 A300508 A120013 * A344180 A151847 A349593

Adjacent sequences: A377152 A377153 A377154 * A377156 A377157 A377158

Keyword

nonn

Author

John Mason, Oct 18 2024

Status

approved