The generating function for P-partitions of the lattice L(a,b) for

                        a=, 2, b=, 2, is the following:

1/(q^4+q^3-q-1)/(q^5-1)/(q^4-1)/(q^3-1)/(q-1)^2
                           The first, 31, terms are

[1, 1, 2, 4, 6, 9, 14, 19, 27, 37, 49, 64, 84, 106, 134, 168, 207, 253, 309,

    371, 445, 530, 626, 736, 863, 1003, 1163, 1343, 1543, 1766, 2017]

      The generating function for P-partitions of the lattice L(a,b) for

                        a=, 3, b=, 2, is the following:

1/(q^5-1)/(q^6+q^5-q-1)/(q^3-1)^2/(q^4-1)^2/(q^7-1)/(q^6-1)/(q-1)^2
                           The first, 31, terms are

[1, 1, 2, 4, 7, 11, 18, 27, 41, 60, 87, 122, 172, 235, 320, 430, 572, 751, 982,

    1268, 1629, 2074, 2625, 3297, 4123, 5118, 6324, 7771, 9506, 11567, 14023]

      The generating function for P-partitions of the lattice L(a,b) for

                        a=, 3, b=, 3, is the following:

(1-q+320*q^39+365*q^56+4*q^9+2*q^8+396*q^51+203*q^33+336*q^40+5*q^10+46*q^21+57
*q^22+9*q^13+10*q^14+66*q^23+16*q^15+20*q^17+19*q^16+29*q^18+9*q^12+35*q^19+4*q
^11+344*q^57+78*q^24+39*q^20+3*q^6+134*q^29+158*q^68+169*q^31+238*q^35+389*q^45
+224*q^34+98*q^26+263*q^36+396*q^47+393*q^46+125*q^70+134*q^69+66*q^75+98*q^72+
111*q^71+57*q^76+125*q^28+q^7+86*q^73+46*q^77+2*q^3+393*q^52+184*q^66+278*q^37+
394*q^49+302*q^38+399*q^48+78*q^74+389*q^53+158*q^30+184*q^32+224*q^64+336*q^58
+302*q^60+320*q^59+263*q^62+278*q^61+238*q^63+344*q^41+383*q^44+372*q^43+399*q^
50+203*q^65+383*q^54+372*q^55+86*q^25+111*q^27+365*q^42+169*q^67+20*q^81+16*q^
83+19*q^82+9*q^85+10*q^84+35*q^79+39*q^78+29*q^80+9*q^86+4*q^87+5*q^88+4*q^89+2
*q^90+2*q^95+q^98-q^97+3*q^92+q^91)/(q^5-q^4-q+1)/(q^4-q^3-q+1)/(q^3+1-q^2-q)^2
/(q^12-1)/(q^11-1)/(q^20-1)/(q^19-1)/(q^18-1)/(q^17-1)/(q^16-1)/(q^15-1)/(q^14-\
1)/(q^13-1)/(q^10-1)/(q^9-1)/(q^7+q^6+q^5+q^4+q^3+q^2+q+1)/(q^6+q^5+q^4+q^3+q^2
+q+1)/(q^2-q+1)/(q^4+q^3+q^2+q+1)
                           The first, 31, terms are

[1, 1, 2, 4, 8, 13, 23, 37, 61, 95, 150, 227, 346, 512, 756, 1097, 1585, 2256,

    3197, 4480, 6245, 8621, 11840, 16134, 21876, 29452, 39457, 52539, 69634,

    91779, 120443]