A286332 Grundy values for 2 X n rectangles in Remove-a-Square game.

0, 2, 2, 1, 4, 3, 3, 1, 4, 2, 6, 5, 0, 2, 7, 1, 4, 3, 3, 1, 4, 7, 7, 5, 0, 2, 8, 4, 4, 6, 3, 1, 8, 7, 7, 5, 0, 2, 2, 1, 4, 6, 3, 1, 8, 2, 7, 5, 0, 2, 8, 1, 4, 6, 3, 1, 4, 2, 7, 5, 0, 2, 8, 1, 4, 6, 3, 1, 8, 7, 7, 5, 0, 2, 8, 1, 4, 6, 3, 1, 8, 2, 7, 5, 0, 2, 8, 1, 4, 6, 3, 1, 8, 2, 7, 5

Offset: 1

Author

Tanya Khovanova and students, May 07 2017

Keywords

• nonn

Comments

Given a 2 X n rectangle on a square grid, players are allowed to remove one cell or a 2 X 2 full square.

a(12n+1) = 0.

The sequence becomes eventually periodic with period 12.

Links

• Pratik Alladi, Neel Bhalla, Tanya Khovanova, Nathan Sheffield, Eddie Song, William Sun, Andrew The, Alan Wang, Naor Wiesel, Kevin Zhang Kevin Zhao, PRIMES STEP Plays Games, arXiv:1707.07201 [math.CO], 2017, Section 7.
• Sierra Brown, Spencer Daugherty, Eugene Fiorini, Barbara Maldonado, Diego Manzano-Ruiz, Sean Rainville, Riley Waechter, and Tony W. H. Wong, Nimber Sequences of Node-Kayles Games, J. Int. Seq., Vol. 23 (2020), Article 20.3.5.