Note: It was previously known that these matroids have h-vectors which are pure O-sequences, thus we have not applied the computer algorithms to generate monomials for them. See our paper for details.

h-vector
(1,6,0)
(1,6,5)
(1,6,6)
(1,6,8)
(1,6,9)
(1,6,10)
(1,6,11)
(1,6,12)
(1,6,13)
(1,6,14)
(1,6,15)
(1,6,16)
(1,6,17)
(1,6,18)
(1,6,19)
(1,6,20)
(1,6,21)