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
(1,3,0,0)
(1,3,2,0)
(1,3,3,0)
(1,3,3,1)
(1,3,3,2)
(1,3,3,3)
(1,3,4,0)
(1,3,4,2)
(1,3,4,4)
(1,3,5,0)
(1,3,5,3)
(1,3,5,4)
(1,3,5,5)
(1,3,5,6)
(1,3,5,7)
(1,3,6,0)
(1,3,6,5)
(1,3,6,6)
(1,3,6,7)
(1,3,6,8)
(1,3,6,9)
(1,3,6,10)