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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 (list; graph; refs; listen; history; text; internal format)



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.


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), 33-46.

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.


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.


Cf. A008810 (maximum number of L-shaped 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




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


a(10)-a(14) from Lars Blomberg, Aug 08 2017

a(15) from Andrey Zabolotskiy, Oct 20 2017



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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)