a(n) is the number of self-avoiding polygons on the n X n square lattice having 2n edges (arbitrary perimeter) with an edge on each of the n distinct horizontal and n distinct vertical lines in the lattice.

a(4)=26: 4 symmetries of the Z pentomino; 4 rotations of the step (123 bargraph) hexomino; 8 symmetries of each of the 132 and 213 bargraph hexominoes; and 2 rotations of the heptomino that consists of a 3x3 square with opposite corner cells removed.