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
(1,4,0)
(1,4,3)
(1,4,4)
(1,4,6)
(1,4,7)
(1,4,8)
(1,4,9)
(1,4,10)