Whether I import a smooth shaded mesh from Blender or I generate a mesh in Unity manually using Unity's built in normal calculation function, I get a square grid pattern showing for the shading of my mesh (red line highlights a couple of the squares).

Each square outline is where a quad is located.

Is this normal? Is there any way that I can make this appear more smooth?

Edit:

Each point on the triangle exists only once. Points are shared between triangles. They are created with a simple loop:

        List<Vector3> vertexList = new List<Vector3>();

        for (int z = 0; z < zSize; z++)
        {
            for (int x = 0; x < xSize; x++)
            {
                Vector3 v = new Vector3(0, 0, 0);
                v.x = (x * vertexSpacing) - vertexSpacing;
                v.z = (z * vertexSpacing) - vertexSpacing;
                v.y = Mathf.PerlinNoise(v.x + g.transform.position.x, v.z + g.transform.position.z);
                vertexList.Add(v);
            }
        }