|
%I #17 Oct 30 2023 13:26:17
%S 0,0,1,2,4,6,8,12,14,18,22,27,32,37,43,49,55,62,69,77
%N The maximum number of V-pentominoes covering the cells of square n × n.
%C 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.
%C 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.
%C Solutions for the squares 3 × 3, 5 × 5, 8 × 8, 12 × 12, 16 × 16 are unique under rotation and reflection.
%D 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
%D A. Cibulis, Pentominoes, Part I, Riga, University of Latvia, 2001, 96 p. (In Latvian)
%D A. Cibulis, From Olympiad Problems to Unsolved Ones, The 12th International Conference "Teaching Mathematics: Retrospective and Perspectives", Šiauliai University, Abstracts, pp. 19-20, 2011.
%e There is no way to cover square 3 × 3 with more than just one V-pentomino so a(3)=1.
%K nonn,more
%O 1,4
%A Juris Čerņenoks, Jul 10 2012
|
