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

Author

John Mason, Oct 18 2024

Keywords

• nonn

Comments

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

Links

• 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.

Crossrefs

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

Formula

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