If you checkerboard color the vertices of the square lattice, a(n) is the number of orthogonal polygons of area n, which alternates between white and black vertices.
Table of n, a(n) for n=1..10.
Giovanni Resta, Illustration of a(10) = 55.
For n=5 the a(5)=2 pentominoes are 'I' and 'X'.
Sequence in context: A190591 A027945 A079800 * A280028 A094271 A194422
Adjacent sequences: A217592 A217593 A217594 * A217596 A217597 A217598
Thomas Dybdahl Ahle, May 28 2013
a(10) from Giovanni Resta, Jun 06 2013