A polyomino is geometric shape consisting of squares that are joined to each other at their edges. The squares may not over lap or be only in partial contact with the squares they connect to.
2 Dimensional polyominos have number of characteristics firstly, the number of squares they contain sometimes called their Mass. Secondly, the longest unbroken straight chain of squares they contain is called their spinelength. Thirdly, all polyominos have a box size this is the area of the smallest possible rectangle that will entirely contain the polyomino.
e.g. A bent triomino would have mass 3, spinelength 2 and boxsize 4.
Although it is difficult to calculate the number of polyominos with mass n it is relatively simple to find a formula for the number of distinct polyominos with spinelength n and mass n+1. If we say that reflections and rotations of polyominos are not distinct then the formula is simply n/2 rounded up to the nearest whole number.
The formula for the number of distinct polyominos with spinelength n and mass n+2 is x(2n-4) +1 where x n/2 rounded up to the nearest whole number.