

A280984


Minimum number of dominoes on an n X n chessboard to prevent placement of another domino.


0



0, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75
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OFFSET

1,2


COMMENTS

Each domino must cover exactly two adjacent squares of a row or column. Sequence inspired by question for 8 X 8 case in "Minimum Guard Problem" link.


LINKS

Table of n, a(n) for n=1..15.
A. Gyárfás, J. Lehel, Zs. Tuza, Clumsy packing of dominoes, Discrete Mathematics, Volume 71, Issue 1 (1988), 3346.
Mathematics Stack Exchange user "Manin", Minimum Guard Problem.
Peter Kagey, Minimum number of dominoes on an n X n chessboard to prevent placement of another domino.


FORMULA

Proved: a(n) >= A008810(n) for n>1; when n = 0 (mod 3), a(n) = A008810(n).  Andrey Zabolotskiy, Oct 22 2017
a(n) > n^2/3 + n/111 for large n not congruent to 0 (mod 3) [from Gyárfás, Lehel, Tuza].  Peter Kagey, May 22 2019.


CROSSREFS

Cf. A008810 (maximum number of Lshaped triominoes with the same orientation in an n X n square).
Sequence in context: A140495 A174873 A213172 * A008810 A176893 A144677
Adjacent sequences: A280981 A280982 A280983 * A280985 A280986 A280987


KEYWORD

nonn,more


AUTHOR

Rick L. Shepherd, Jan 11 2017, Aug 06 2017


EXTENSIONS

a(10)a(14) from Lars Blomberg, Aug 08 2017
a(15) from Andrey Zabolotskiy, Oct 20 2017


STATUS

approved



