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
(1,7,0)
(1,7,6)
(1,7,7)
(1,7,10)
(1,7,12)
(1,7,13)
(1,7,15)
(1,7,16)
(1,7,17)
(1,7,18)
(1,7,19)
(1,7,20)
(1,7,21)
(1,7,22)
(1,7,23)
(1,7,24)
(1,7,25)
(1,7,26)
(1,7,27)
(1,7,28)