Let \(T_{n-1} = 28\), \(T_n = 56\), and \(T_{n+1} = 70\). Let A \((4\cos t, 4\sin t)\), B \((2\sin t, -2\cos t)\), and C \((3r_n - 1, r^2_n - n - 1)\) be the vertices of a triangle ABC, where \(t\) is a parameter. If \((3x - 1)^2 + (3y)^2 = a\), is the locus of the centroid of triangle ABC, then \(a\) equals: