A093426 Number of different two-dimensional burst patterns in the hexagonal graph.

1, 4, 21, 118, 690, 4145

Offset

1,2

Comments

The hexagonal graph has vertices which are the centers of identical regular hexagons tiling the plane and the centers of adjacent hexagons are connected. Alternatively, we can use an isomorphic representation in which the vertices are the elements of Z^2 and (x,y) is connected to (x-1,y),(x+1,y),(x,y-1),(x,y+1),(x-1,y-1),(x+1,y+1). A cluster of size t is a set of t points such that each pair of points of the set is on a connected path contained entirely within the set. A burst pattern is a labeling of Z^2 with 0's and 1's. The term a(n) denotes the number of different (up to a translation) burst patterns whose 1's are covered by a cluster of size n.

Links

Table of n, a(n) for n=1..6.

M. Blaum, J. Bruck, and A. Vardy, Interleaving schemes for multidimensional cluster errors, IEEE Trans. on Inform. Theory 44(2) (1998), 730-743.

Tuvi Etzion and Alexander Vardy, Two-dimensional interleaving schemes with repetitions: constructions and bounds, IEEE Trans. on Inform. Theory, 48(2) (2002), 428-457.

Moshe Schwartz and Tuvi Etzion, Two-dimensional burst-correcting codes, Proceedings, International Symposium on Information Theory, 2004.

Example

a(2) = 4 because we have the following burst patterns (the *'s indicate the 1's):
1) *
2) **
3) *
...*
4) .*
...*

Crossrefs

Cf. A093424, A093427.

Sequence in context: A212419 A020048 A318365 * A182435 A046090 A045721

Adjacent sequences: A093423 A093424 A093425 * A093427 A093428 A093429

Keyword

nonn,more

Author

Tuvi Etzion and Moshe Schwartz (etzion(AT)cs.technion.ac.il), May 11 2004

Status

approved