Convex n-ominoes

Unit squares having their vertices at integer points in the Carresian plane are called cells. A connected union of n distinct cells having no finite cut set is an n-omino. Two n-ominoes are the same if one is mapped onto the other by a translation of the plane. An n-omino is convex if the cells in each row and each column to an a connected strip. When viewed from a distance, most convex n-ominoes resemble rods tilted 45° from the vertical with horizontal (and vertical) thickness roughly equal to 2.37597. If c(n) denotes the number of convex n-ominoes, then c(n) ～ fyⁿ, where y = 2.30914 and f = 2.67564. (It is understood that all constants are accurate to within -$\text{1}\text{2}$ in the last place.)