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

1,2

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

Table of n, a(n) for n=1..96.

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.

Crossrefs

Sequence in context: A305326 A122918 A177424 * A248755 A129903 A263203

Adjacent sequences: A286329 A286330 A286331 * A286333 A286334 A286335

Keyword

nonn

Author

Tanya Khovanova and students, May 07 2017

Status

approved