A214294 The maximum number of V-pentominoes covering the cells of square n X n.

0, 0, 1, 2, 4, 6, 8, 12, 14, 18, 22, 27, 32, 37, 43, 49, 55, 62, 69, 77

Offset: 1

Author

Juris Cernenoks, Jul 10 2012

Keywords

• nonn
• more
• changed

Comments

The problem of determining the maximum number of V-pentominoes (or the densest packing) covering the cells of the square n X n was proposed by A. Cibulis.

Problem for the squares 5 X 5, 6 X 6 and 8 X 8 was given in the Latvian Open Mathematics Olympiad 2000 for Forms 6, 8 and 5 respectively.

Solutions for the squares 3 X 3, 5 X 5, 8 X 8, 12 X 12, 16 X 16 are unique under rotation and reflection.

Examples

			There is no way to cover square 3 X 3 with more than just one V-pentomino so a(3)=1.
		

References

• A. Cibulis, Equal Pentominoes on the Chessboard, j. "In the World of Mathematics", Kyiv, Vol. 4., No. 3, pp. 80-85, 1998. (In Ukrainian), http://www.probability.univ.kiev.ua/WorldMath/mathw.html
• A. Cibulis, Pentominoes, Part I, Riga, University of Latvia, 2001, 96 p. (In Latvian)
• A. Cibulis, From Olympiad Problems to Unsolved Ones, The 12th International Conference "Teaching Mathematics: Retrospective and Perspectives", Šiauliai University, Abstracts, pp. 19-20, 2011.