A093427 Number of different two-dimensional burst patterns in the grid graph with eight neighbors.

1, 5, 33, 239, 1814, 14166

Offset

1,2

Comments

The grid graph with eight neighbors has Z^2 as vertices and each vertex (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),(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) = 5 because we have the following burst patterns (the *'s mark the 1's):
1) *
2) **
3) *
...*
4) .*
...*
5) *
....*

Crossrefs

Cf. A093424, A093426.

Sequence in context: A001887 A118803 A284734 * A142989 A084131 A084771

Adjacent sequences: A093424 A093425 A093426 * A093428 A093429 A093430

Keyword

nonn,more

Author

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

Status

approved