  The elliptic genus Z_{BH} of a large class of 4D black holes can be expressed
as an M-theory partition function on an AdS_3xS^2xCY_3 attractor. We
approximate this partition function by summing over multiparticle chiral
primary states of membranes which wrap curves in the CY_3 and tile Landau
levels on the horizon S^2. Significantly, membranes and antimembranes can
preserve the same supercharges if they occupy antipodal points on the horizon.
It is shown the membrane contribution to Z_{BH} gives precisely the topological
string partition function Z_{top} while the antimembranes give \bar Z_{top},
implying Z_{BH}=|Z_{top}|^2 in this approximation.
