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
Andrejs Cibulis and Walter Trump, Domino Exclusion Problem, Baltic J. Modern Computing, Vol. 8 (2020), No. 4, 496-519.
A. Gyárfás, J. Lehel, and Zs. Tuza, Clumsy packing of dominoes, Discrete Mathematics, Volume 71, Issue 1 (1988), 33-46.
Peter Kagey, Minimum number of dominoes on an n X n chessboard to prevent placement of another domino.
Mathematics Stack Exchange user "Manin", Minimum Guard Problem.
Walter Trump, Minimum Domino Packing
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
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
a(16)-a(17) from Rob Pratt (see the link to Peter Kagey's question) and a(18) added by Andrey Zabolotskiy, Feb 13 2020
a(19)-a(33) from Walter Trump, Jun 14 2020
STATUS
approved