Domino Exclusion Problem

The classic domino exclusion problem consists of finding minimum number d(n) of dominoes on an n × n chessboard to prevent placement of another domino. This sequence of minimum numbers is discussed under A280984 at the On-Line Encyclopedia of Integer Sequences. With new theoretical insights and a specially designed computer program we were able to expand the sequence from n =18 to n = 33. New upper bounds of d(n) thought to be sharp have been obtained. The article also discusses the rectangle-free minimal domino packings. Small 3-dimensional grid squares up to n = 6 have been analysed.