Full list of non-zero Kazhdan-Lusztig-Vogan polynomials:

 0:  0: 1

 1:  0: 1
     1: 1

 2:  0: 1
     2: 1

 3:  0: 1
     3: 1

 4:  0: 1
     1: 1
     2: 1
     4: 1

 5:  0: 1
     1: 1
     2: 1
     5: 1

 6:  0: 1
     2: 1
     3: 1
     6: 1

 7:  0: 1
     1: 1
     3: 1
     7: 1

 8:  0: 1
     2: 1
     3: 1
     8: 1

 9:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     6: 1
     7: 1
     9: 1

10:  0: 1
     1: 1
     2: 1
     4: 1
     5: 1
    10: 1

11:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     6: 1
     7: 1
    11: 1

12:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     7: 1
     8: 1
    12: 1

13:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     7: 1
     8: 1
    13: 1

14:  0: 1
     2: 1
     3: 1
     6: 1
     8: 1
    14: 1

15:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     9: 1
    10: 1
    11: 1
    15: 1

16:  0: q+1
     1: 1
     2: q+1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
    10: 1
    11: 1
    12: 1
    14: 1
    16: 1

17:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     6: 1
     7: 1
     8: 1
     9: 1
    12: 1
    14: 1
    17: 1

18:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     7: 1
     8: 1
    10: 1
    12: 1
    13: 1
    18: 1

19:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     6: 1
     7: 1
     8: 1
    11: 1
    13: 1
    14: 1
    19: 1

20:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
     9: 1
    10: 1
    11: 1
    12: 1
    14: 1
    15: 1
    16: 1
    17: 1
    20: 1

21:  0: q+1
     1: q+1
     2: 1
     3: q+1
     4: 1
     5: 1
     6: 1
     7: q+1
     8: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    14: 1
    15: 1
    17: 1
    18: 1
    19: 1
    21: 1

22:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
    10: 1
    11: 1
    12: 1
    13: 1
    14: 1
    16: 1
    18: 1
    19: 1
    22: 1

23:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    14: 1
    15: 1
    16: 1
    17: 1
    18: 1
    19: 1
    20: 1
    21: 1
    22: 1
    23: 1

213 nonzero polynomials, and 0 zero polynomials,
 at 213 Bruhat-comparable pairs.