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

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

Offset

1,4

Comments

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

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

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

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.

Links

Table of n, a(n) for n=1..20.

Example

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

Crossrefs

Sequence in context: A089623 A089681 A227308 * A233578 A057220 A294847

Adjacent sequences: A214291 A214292 A214293 * A214295 A214296 A214297

Keyword

nonn,more

Author

Juris Čerņenoks, Jul 10 2012

Status

approved