A note on triangle-free distance-regular graphs with a2≠0

Let Γ denote a distance-regular graph with classical parameters (D,b,α,β) and D⩾3. Assume the intersection numbers a1=0 and a2≠0. We show that the intersection number c2 is either 1 or 2, and if c2=1, then (b,α,β)=(−2,−2,((−2)D+1−1)/3).