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Number of path covers of an n X n grid.
0

%I #2 Feb 19 2004 03:00:00

%S 1,15,1803,2015052,20582691507,1928747601908977,

%T 1657680158728377785062,13067714049552363383420892169,

%U 944866406096482421853329114821597865

%N Number of path covers of an n X n grid.

%C A path cover is set of disjoint paths such that each node of the graph belongs to exactly one of these. A Hamiltonian path is a special path cover consisting of a single path. Paths of length zero (i.e. single nodes) are permitted.

%e a(1) = 1 as there is only the trivial cover by a single path of length 0

%e a(2) = 15 = 1 (all length 0) + 4 (2x0, 1x1) + 2 (2x1) + 4 (1x2, 1x0) + 4 (1x3)

%K nonn

%O 1,2

%A Andre Poenitz (poenitz(AT)htwm.de), Nov 26 2003