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A070862 Number of path covers of an n X n grid. 1
1, 15, 1803, 2015052, 20582691507, 1928747601908977, 1657680158728377785062, 13067714049552363383420892169, 944866406096482421853329114821597865 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

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

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

CROSSREFS

Sequence in context: A069450 A205346 A208868 * A077730 A110103 A232305

Adjacent sequences:  A070859 A070860 A070861 * A070863 A070864 A070865

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)