Counting polyominoes: Yet another attack

A polyomino is a connected collection of squares on an unbounded chessboard. There is no known formula yielding the number of distinct polyominoes of a given number of squares A polyomino enumeration method, faster than any previous, is presented. This method includes the calculation of the number of symmetric polyominoes. All polyominoes containing up to 24 squares have been enumerated (using ten months of computer time). Previously, only polyominoes up to size 18 were enumerated.