A180604 Number of "pieces" of the n-th Brillouin zone of a 2D hexagonal lattice.

1, 6, 6, 6, 12, 18, 30, 30, 18, 18, 36, 42, 54, 54, 42, 66

Offset: 1

Author

Keenan Pepper, Sep 11 2010

Keywords

• nonn
• more

Comments

Each Brillouin zone has the same area, and they are all equivalent mod the periodicity of the lattice, but the higher-order ones consist of a set of polygons. This is the number of polygons in that set.

Examples

			The 2nd Brillouin zone consists of 6 equilateral triangles, so a(2) = 6. The 5th Brillouin zone consists of 12 30-60-90 triangles, so a(5) = 12.