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A093424
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Number of different two-dimensional burst patterns in the grid graph: The grid graph 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). 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.
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2
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OFFSET
| 1,2
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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.
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EXAMPLE
| a(3)=13 because we have the following burst patterns: (*'s indicate the 1's)
1) *
2) **
3) *.*
4) *
...*
5) *
...*
6) *
....*
7) .*
...*
8) ***
9) **
....*
10) *
....**
11) .*
....**
12) **
....*
13) *
....*
....*
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CROSSREFS
| Cf. A093426, A093427.
Sequence in context: A074548 A141786 A122122 * A186242 A092467 A034478
Adjacent sequences: A093421 A093422 A093423 * A093425 A093426 A093427
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KEYWORD
| nonn
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AUTHOR
| Tuvi Etzion and Moshe Schwartz (etzion(AT)cs.technion.ac.il), May 11 2004
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