We solve the conjecture by R. Fenn, C. Rourke and B. Sanderson that the rack homology of dihedral quandles satisfies for odd prime [T. Ohtsuki, Problems on invariants of knots and 3-manifolds, Geom. Topol. Monogr. 4 (2002) 377-572, Conjecture 5.12]. We also show that contains for . Furthermore, we show that the torsion of is annihilated by 3. We also prove that the quandle homology contains for odd prime. We conjecture that for quandle homology satisfies: , where are “delayed” Fibonacci numbers, that is, and . Our paper is the first step in approaching this conjecture.