|
| |
|
|
A093427
|
|
Number of different two-dimensional burst patterns in the grid graph with eight neighbors: 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.
|
|
2
| | |
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| M. Blaum, J. Bruck, A. Vardy, "Interleaving schemes for multidimensional cluster errors", IEEE Trans. on Inform. Theory, 44(2):730-743, March 1998.
Tuvi Etzion and Alexander Vardy, "Two-dimensional interleaving schemes with repetitions: constructions and bounds", IEEE Trans. on Inform. Theory, 48(2):428-457, 2002.
Moshe Schwartz and Tuvi Etzion, "Two-dimensional burst-correcting codes", in preparation.
|
|
|
EXAMPLE
| a(2)=5 because we have the following burst patterns: (*'s mark the 1's)
1) *
2) **
3) *
...*
4) .*
...*
5) *
....*
|
|
|
CROSSREFS
| Cf. A093424, A093426.
Sequence in context: A128418 A001887 A118803 * A142989 A084131 A084771
Adjacent sequences: A093424 A093425 A093426 * A093428 A093429 A093430
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Tuvi Etzion and Moshe Schwartz (etzion(AT)cs.technion.ac.il), May 11 2004
|
| |
|
|
