cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A280984 Minimum number of dominoes on an n X n chessboard needed to prevent placement of another domino.

Original entry on oeis.org

0, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75, 86, 97, 108, 122, 134, 147, 163, 178, 192, 210, 227, 243, 263, 282, 300, 322, 343, 363
Offset: 1

Views

Author

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

Keywords

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.
A.k.a. lower matching number of the n X n grid graph. - Eric W. Weisstein, Dec 16 2024
a(n) = 0 for n = 1, a(n) = ceiling(n^2/3) + 1 for n = 19, 22, 23, 25, 26, 28, 29, 31, 32, and a(n) = ceiling(n^2/3) for other n <= 32. - Eric W. Weisstein, Dec 16 2024

Links

Crossrefs

Cf. A008810 (maximum number of L-shaped trominoes with the same orientation in an n X n square, a.k.a. ceil(n^2/3)).
Cf. A378763 (lower matching number of the n X n torus grid graph).
Cf. A379177 (lower matching number of the n X n X n grid graph).

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

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
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