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A347554
Number of minimum dominating sets in the n X n king graph.
2
1, 4, 1, 256, 79, 1, 243856, 3600, 1, 581571283, 281585, 1, 2722291223553, 32581328, 1, 21706368614058886, 5112264019, 1, 268740319616196074546, 1028516654620, 1, 4839916638142874877046813
OFFSET
1,2
COMMENTS
a(3*n) = 1 for all n, since the 3n X 3n king graph has domination number n^2 and the only way to achieve this is if each of the n^2 kings is placed in the middle of its own 3 X 3 square.
LINKS
Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], Aug 2024.
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Minimum Dominating Set
CROSSREFS
Main diagonal of A350815.
Cf. A075561 (domination number of the n X n king graph), A133791, A286881.
Sequence in context: A262404 A299522 A300140 * A298939 A240098 A094337
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Sep 06 2021
EXTENSIONS
a(7)-a(12) from Andrew Howroyd, Jan 17 2022
a(13)-a(22) from Stephan Mertens, Aug 18 2024
STATUS
approved