This is the story for generating functions in , q,  for Solid

              partitions bounded in a 2 by 2 by n by infinity box

                            for n between 2 and , 5

            as well as the first , 31, terms in the counting series

           The generating function in, q,  when n=, 2,  happens to be

(3*q^12+2*q^13+4*q^9+3*q^11+2*q^14+4*q^7+3*q^4+1+2*q^2+q^16+2*q^3+5*q^6+3*q^5+8
*q^8+5*q^10)/(q-1)/(q^2-1)/(q^3-1)/(q^4-1)/(q^5-1)/(q^6-1)/(q^7-1)/(q^8-1)
                           The first, 31,  terms are

[1, 1, 4, 7, 14, 23, 41, 63, 104, 152, 230, 327, 470, 647, 897, 1202, 1616,

    2117, 2775, 3566, 4580, 5787, 7301, 9092, 11298, 13885, 17028, 20688, 25076,

    30154, 36172]

           The generating function in, q,  when n=, 3,  happens to be

(1+2*q^34+11*q^30+23*q^28+6*q^31+81*q^20+70*q^21+70*q^15+83*q^19+83*q^17+54*q^
23+26*q^27+63*q^22+36*q^10+5*q^4+26*q^9+40*q^11+63*q^14+40*q^25+3*q^3+6*q^5+11*
q^6+14*q^7+23*q^8+49*q^12+36*q^26+2*q^2+81*q^16+54*q^13+3*q^33+q^36+92*q^18+14*
q^29+5*q^32+49*q^24)/(q^4-1)/(q^8+q^6-q^2-1)/(q^11-1)/(q^10-1)/(q^9-1)/(q^6-q^4
+q^2-1)/(q^7-1)/(q^6-1)/(q^5-1)/(q-1)/(q^3-1)/(q^2-1)
                           The first, 31,  terms are

[1, 1, 4, 8, 17, 30, 58, 97, 171, 276, 450, 697, 1081, 1617, 2414, 3512, 5082,

    7209, 10167, 14103, 19443, 26456, 35771, 47844, 63613, 83785, 109737,

    142569, 184236, 236400, 301831]

           The generating function in, q,  when n=, 4,  happens to be

(1+6008*q^34+4541*q^30+3695*q^28+4906*q^31+1101*q^20+1305*q^21+336*q^15+888*q^
19+565*q^63+3252*q^53+565*q^17+4089*q^51+7082*q^39+1828*q^23+4541*q^50+7164*q^
40+6585*q^44+5328*q^48+6008*q^46+6781*q^37+7003*q^38+2163*q^56+6781*q^43+730*q^
62+3695*q^52+3252*q^27+6272*q^35+1571*q^22+78*q^10+6*q^4+50*q^9+102*q^11+262*q^
14+2476*q^25+3*q^3+8*q^5+15*q^6+21*q^7+38*q^8+147*q^12+2878*q^26+2*q^2+451*q^16
+189*q^13+5641*q^33+6585*q^36+730*q^18+4089*q^29+78*q^70+1101*q^60+38*q^72+102*
q^69+1305*q^59+15*q^74+451*q^64+8*q^75+888*q^61+2878*q^54+5328*q^32+336*q^65+
2163*q^24+50*q^71+6*q^76+262*q^66+3*q^77+1828*q^57+5641*q^47+2*q^78+21*q^73+q^
80+147*q^68+189*q^67+7082*q^41+4906*q^49+2476*q^55+7003*q^42+6272*q^45+1571*q^
58)/(q^6-1)/(q^7-1)/(q^14-1)/(q^8-1)/(q^11-1)/(q^16-1)/(q^15-1)/(q^13-1)/(q^12-\
1)/(q^10-1)/(q^9-1)/(q-1)/(q^5-1)/(q^2-1)/(q^4-1)/(q^3-1)
                           The first, 31,  terms are

[1, 1, 4, 8, 18, 33, 65, 114, 208, 350, 595, 964, 1560, 2441, 3803, 5786, 8745,

    12977, 19119, 27750, 39978, 56888, 80362, 112350, 155998, 214661, 293503,

    398166, 536919, 719001, 957469]

           The generating function in, q,  when n=, 5,  happens to be

(1+40688*q^34+21371*q^30+14792*q^28+25340*q^31+2502*q^20+3200*q^21+46851*q^85+
34975*q^87+61099*q^83+96938*q^79+5163*q^97+573*q^15+1901*q^19+77822*q^81+250875
*q^63+224935*q^53+1073*q^17+206651*q^51+77822*q^39+2*q^118+3*q^117+5163*q^23+
196704*q^50+87184*q^40+129383*q^44+175079*q^48+152293*q^46+61099*q^37+69239*q^
38+246171*q^56+118109*q^43+254591*q^62+216281*q^52+12134*q^27+46851*q^35+4108*q
^22+101*q^10+6*q^4+63*q^9+143*q^11+422*q^14+8035*q^25+3*q^3+9*q^5+17*q^6+24*q^7
+45*q^8+212*q^12+9949*q^26+2*q^2+801*q^16+292*q^13+34975*q^33+53742*q^36+1452*q
^18+17800*q^29+196704*q^70+257498*q^60+175079*q^72+206651*q^69+256640*q^59+
152293*q^74+246171*q^64+140673*q^75+256640*q^61+233053*q^54+29951*q^32+239995*q
^65+6499*q^24+185962*q^71+129383*q^76+233053*q^66+118109*q^77+250875*q^57+
163656*q^47+107389*q^78+163656*q^73+40688*q^86+1452*q^102+53742*q^84+1901*q^101
+25340*q^89+4108*q^98+21371*q^90+422*q^106+101*q^110+6499*q^96+2502*q^100+87184
*q^80+17*q^114+9*q^115+3200*q^99+17800*q^91+45*q^112+801*q^104+212*q^108+573*q^
105+143*q^109+292*q^107+63*q^111+12134*q^93+9949*q^94+8035*q^95+1073*q^103+
216281*q^68+29951*q^88+224935*q^67+96938*q^41+185962*q^49+239995*q^55+107389*q^
42+140673*q^45+254591*q^58+14792*q^92+q^120+24*q^113+69239*q^82+6*q^116)/(q^13-\
1)/(q^4-1)^3/(q^5-1)^2/(q^18-1)/(q^14-1)/(q^10-1)/(q^15-1)/(q^8-q^7+q^6-q^5+q^3
-q^2+q-1)/(q^19-1)/(q^17-1)/(q^14-q^12+q^10-q^8+q^6-q^4+q^2-1)/(q^10-q^8+q^6-q^
4+q^2-1)/(q^11-1)/(q^9-1)/(q^6-q^4+q^2-1)/(q-1)/(q^7-1)/(q^2+q+1)^2/(q^2-q+1)
                           The first, 31,  terms are

[1, 1, 4, 8, 18, 34, 68, 121, 225, 387, 672, 1116, 1848, 2967, 4739, 7400,

    11473, 17488, 26451, 39455, 58401, 85441, 124065, 178374, 254642, 360391,

    506702, 707009, 980446, 1350440, 1849432]

              The whole thing took, 169.390, seconds of CPU time