We want to compute the Kazhdan-Lusztig polynomials of a Dihedral group $D_n$.
I understand that they are of the form $$(1,v,v,v^2,v^2,v^3,v^3,\cdots,v^k)$$ and am able to show it by hands in small cases, but I can't see a way to prove it all together!
Thanks!