Parabolic R-polynomials were introduced by Deodhar as parabolic analogues of ordinary R-polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the computation of parabolic R A0;-polynomials for the symmetric group. Let a0fa" title="Click to view the MathML source">Sn be the symmetric group on e5dd38c" title="Click to view the MathML source">{1,2,…,n}, and let e4443ee8e8752445f9fa0"> be the generating set of a0fa" title="Click to view the MathML source">Sn, where for a0684f505038d0ef09931" title="Click to view the MathML source">1≤i≤n−1, bce61a2a7eef932" title="Click to view the MathML source">si is the adjacent transposition. For a subset 84fd342a67cad6a5" title="Click to view the MathML source">J⊆S, let e6f697f546828c6f758" title="Click to view the MathML source">(Sn)J be the parabolic subgroup generated by J , and let e6cf431e93" title="Click to view the MathML source">(Sn)J be the set of minimal coset representatives for Sn/(Sn)J. For e611642a1f7b5f38" title="Click to view the MathML source">u≤v∈(Sn)J in the Bruhat order and 848463b399d953e052589" title="Click to view the MathML source">x∈{q,−1}, let e461543c2f6456"> denote the parabolic R-polynomial indexed by u and v . Brenti found a formula for e461543c2f6456"> when J=S∖{si}, and obtained an expression for e461543c2f6456"> when 849ad9145ad785893c3a846c30" title="Click to view the MathML source">J=S∖{si−1,si}. In this paper, we provide a formula for e461543c2f6456">, where J=S∖{si−2,si−1,si} and i appears after i−1 in v. It should be noted that the condition that i appears after i−1 in v is equivalent to that v is a permutation in (Sn)S∖{si−2,si}. We also pose a conjecture for e461543c2f6456">, where J=S∖{sk,sk+1,…,si} with 1≤k≤i≤n−1 and v is a permutation in (Sn)S∖{sk,si}.