

A214294


The maximum number of Vpentominoes covering the cells of square n × n.


0



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

1,4


COMMENTS

The problem of determining the maximum number of Vpentominoes (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. 8085, 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. 1920, 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 Vpentomino so a(3)=1.


CROSSREFS

Sequence in context: A089623 A089681 A227308 * A233578 A057220 A294847
Adjacent sequences: A214291 A214292 A214293 * A214295 A214296 A214297


KEYWORD

nonn


AUTHOR

Juris Čerņenoks, Jul 10 2012


STATUS

approved



