A180603 Number of "pieces" of the n-th Brillouin zone of a 2D square lattice.

1, 4, 8, 12, 20, 20, 12, 12, 20, 28, 44, 48, 48

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 4 right isosceles triangles, so a(2) = 4. The 4th Brillouin zone consists of 8 triangles and 4 kites, so a(4) = 12.
		

Links

• Jaroslaw W. Klos, 2D Brillouin Zones, Wolfram Demonstrations Project, 2013.

Crossrefs

Cf. A180604, A199765, A199766.