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
(1,6,0,0)
(1,6,5,0)
(1,6,6,0)
(1,6,6,5)
(1,6,6,6)
(1,6,8,0)
(1,6,9,0)
(1,6,9,4)
(1,6,10,0)
(1,6,10,5)
(1,6,10,8)
(1,6,10,10)
(1,6,11,0)
(1,6,11,6)
(1,6,11,10)
(1,6,11,11)
(1,6,11,12)
(1,6,11,15)
(1,6,11,16)
(1,6,12,0)
(1,6,12,8)
(1,6,12,9)
(1,6,12,12)
(1,6,13,0)
(1,6,13,8)
(1,6,13,12)
(1,6,13,16)
(1,6,14,0)
(1,6,14,9)
(1,6,14,10)
(1,6,14,12)
(1,6,14,13)
(1,6,14,14)
(1,6,14,15)
(1,6,14,16)
(1,6,14,18)
(1,6,14,20)
(1,6,14,21)
(1,6,14,22)
(1,6,15,0)
(1,6,15,10)
(1,6,15,11)
(1,6,15,12)
(1,6,15,14)
(1,6,15,15)
(1,6,15,18)
(1,6,15,19)
(1,6,15,20)
(1,6,15,21)
(1,6,15,22)
(1,6,15,23)
(1,6,15,24)
(1,6,15,26)
(1,6,15,27)
(1,6,15,28)
(1,6,16,0)
(1,6,16,11)
(1,6,16,13)
(1,6,16,14)
(1,6,16,16)
(1,6,16,18)
(1,6,16,20)
(1,6,16,21)
(1,6,16,22)
(1,6,16,24)
(1,6,16,25)
(1,6,16,26)
(1,6,16,28)
(1,6,17,0)
(1,6,17,12)
(1,6,17,14)
(1,6,17,15)
(1,6,17,16)
(1,6,17,17)
(1,6,17,18)
(1,6,17,20)
(1,6,17,21)
(1,6,17,22)
(1,6,17,23)
(1,6,17,24)
(1,6,17,25)
(1,6,17,26)
(1,6,17,27)
(1,6,17,28)
(1,6,17,29)
(1,6,17,30)
(1,6,17,31)
(1,6,17,32)
(1,6,17,33)
(1,6,17,34)
(1,6,18,0)
(1,6,18,13)
(1,6,18,15)
(1,6,18,16)
(1,6,18,17)
(1,6,18,18)
(1,6,18,20)
(1,6,18,22)
(1,6,18,23)
(1,6,18,24)
(1,6,18,25)
(1,6,18,26)
(1,6,18,27)
(1,6,18,28)
(1,6,18,29)
(1,6,18,30)
(1,6,18,31)
(1,6,18,32)
(1,6,18,33)
(1,6,18,34)
(1,6,18,35)
(1,6,18,36)
(1,6,18,37)
(1,6,18,38)
(1,6,18,39)
(1,6,18,40)
(1,6,19,0)
(1,6,19,14)
(1,6,19,17)
(1,6,19,18)
(1,6,19,19)
(1,6,19,24)
(1,6,19,25)
(1,6,19,26)
(1,6,19,27)
(1,6,19,28)
(1,6,19,29)
(1,6,19,30)
(1,6,19,31)
(1,6,19,32)
(1,6,19,33)
(1,6,19,34)
(1,6,19,35)
(1,6,19,36)
(1,6,19,37)
(1,6,19,38)
(1,6,19,39)
(1,6,19,40)
(1,6,19,41)
(1,6,19,42)
(1,6,19,43)
(1,6,19,44)
(1,6,20,0)
(1,6,20,15)
(1,6,20,18)
(1,6,20,19)
(1,6,20,20)
(1,6,20,27)
(1,6,20,28)
(1,6,20,30)
(1,6,20,31)
(1,6,20,32)
(1,6,20,33)
(1,6,20,34)
(1,6,20,35)
(1,6,20,36)
(1,6,20,37)
(1,6,20,38)
(1,6,20,39)
(1,6,20,40)
(1,6,20,41)
(1,6,20,42)
(1,6,20,43)
(1,6,20,44)
(1,6,20,45)
(1,6,20,46)
(1,6,20,47)
(1,6,20,48)
(1,6,20,49)
(1,6,20,50)
(1,6,21,0)
(1,6,21,20)
(1,6,21,21)
(1,6,21,32)
(1,6,21,33)
(1,6,21,34)
(1,6,21,35)
(1,6,21,36)
(1,6,21,39)
(1,6,21,40)
(1,6,21,41)
(1,6,21,42)
(1,6,21,43)
(1,6,21,44)
(1,6,21,45)
(1,6,21,46)
(1,6,21,47)
(1,6,21,48)
(1,6,21,49)
(1,6,21,50)
(1,6,21,51)
(1,6,21,52)
(1,6,21,53)
(1,6,21,54)
(1,6,21,55)
(1,6,21,56)