|
%I #13 Oct 22 2019 07:47:49
%S 1,5,33,239,1814,14166
%N Number of different two-dimensional burst patterns in the grid graph with eight neighbors.
%C 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.
%H M. Blaum, J. Bruck, and A. Vardy, <a href="http://dx.doi.org/10.1109/18.661516">Interleaving schemes for multidimensional cluster errors</a>, IEEE Trans. on Inform. Theory 44(2) (1998), 730-743.
%H Tuvi Etzion and Alexander Vardy, <a href="http://dx.doi.org/10.1109/18.978765">Two-dimensional interleaving schemes with repetitions: constructions and bounds</a>, IEEE Trans. on Inform. Theory, 48(2) (2002), 428-457.
%H Moshe Schwartz and Tuvi Etzion, <a href="http://dx.doi.org/10.1109/ISIT.2004.1365434">Two-dimensional burst-correcting codes</a>, Proceedings, International Symposium on Information Theory, 2004.
%e a(2) = 5 because we have the following burst patterns (the *'s mark the 1's):
%e 1) *
%e 2) **
%e 3) *
%e ...*
%e 4) .*
%e ...*
%e 5) *
%e ....*
%Y Cf. A093424, A093426.
%K nonn,more
%O 1,2
%A Tuvi Etzion and Moshe Schwartz (etzion(AT)cs.technion.ac.il), May 11 2004
|
