The generating function for P-partitions of the lattice L(n) for n=

                              1, is the following:

1/(q-1)^2/(q+1)
                           The first, 41, terms are

[1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12,

    13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21]

      The generating function for P-partitions of the lattice L(n) for n=

                              2, is the following:

1/(q-1)^4/(q+1)^2/(q^2+q+1)/(q^2+1)
                           The first, 41, terms are

[1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 27, 34, 39, 47, 54, 64, 72, 84, 94, 108,

    120, 136, 150, 169, 185, 206, 225, 249, 270, 297, 321, 351, 378, 411, 441,

    478, 511, 551, 588, 632]

      The generating function for P-partitions of the lattice L(n) for n=

                              3, is the following:

1/(q-1)^8/(q+1)^4/(q^2+1)^2/(q^6+q^5+q^4+q^3+q^2+q+1)/(q^2+q+1)^2/(q^2-q+1)/(q^
4+q^3+q^2+q+1)
                           The first, 41, terms are

[1, 1, 2, 3, 6, 8, 13, 18, 27, 36, 51, 67, 92, 118, 156, 198, 256, 319, 404,

    498, 620, 755, 926, 1116, 1353, 1615, 1935, 2291, 2720, 3194, 3759, 4384,

    5120, 5932, 6879, 7923, 9131, 10458, 11981, 13654, 15561]

      The generating function for P-partitions of the lattice L(n) for n=

                              4, is the following:

1/(q-1)^16/(q+1)^8/(q^2+1)^4/(q^4+1)^2/(q^4+q^3+q^2+q+1)^3/(q^4-q^3+q^2-q+1)/(q
^2+q+1)^4/(q^6+q^5+q^4+q^3+q^2+q+1)^2/(q^2-q+1)^2/(1+q^10+q^9+q^8+q^7+q^6+q^5+q
^4+q^3+q^2+q)/(q^6+q^3+1)
                           The first, 41, terms are

[1, 1, 2, 3, 6, 9, 15, 22, 35, 50, 75, 106, 154, 213, 300, 410, 565, 759, 1026,

    1361, 1811, 2373, 3112, 4033, 5226, 6703, 8589, 10915, 13850, 17448, 21942,

    27423, 34206, 42435, 52533, 64726, 79578, 97418, 119002, 144812, 175845]