Lovelock type gravity and small black holes in heterotic string theory

We analyze near horizon behavior of small D-dimensional 2-charge black holes by modifying tree level effective action of heterotic string with all extended Gauss-Bonnet densities. We show that there is a nontrivial and unique choice of parameters, independent of D, for which the black hole entropy in any dimension is given by 4\pi\sqrt{nw}, which is exactly the statistical entropy of 1/2-BPS states of heterotic string compactified on T^{9-D}\times S^1 with momentum n and winding w. This extends the results of Sen [JHEP 0507 (2005) 073] to all dimensions. We also show that our Lovelock type action belongs to the more general class of actions sharing the simmilar behaviour on the AdS_2\times S^{D-2} near horizon geometry.