login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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), 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.

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 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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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