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
(1,5,0)
(1,5,4)
(1,5,5)
(1,5,6)
(1,5,8)
(1,5,9)
(1,5,10)
(1,5,11)
(1,5,12)
(1,5,13)
(1,5,14)
(1,5,15)