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

1,2

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.

Links

Table of n, a(n) for n=1..13.

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

Example

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.

Crossrefs

Cf. A180604, A199765, A199766.

Sequence in context: A337746 A026042 A196377 * A311649 A311650 A311651

Adjacent sequences: A180600 A180601 A180602 * A180604 A180605 A180606

Keyword

nonn,more

Author

Keenan Pepper, Sep 11 2010

Status

approved