#These are the case m=1..6, for the  generating functions for the tiling an m by n rectangle
#by rectangular tiles according to the weight w^NumberOfParticipatingEdges
L:=
[-(w^4*x-w^3*x-w^2*x+1)/(w^3*x+w^2*x-1), -(2*w^10*x^2+2*w^9*x^2-2*w^8*x^2-2*w^7
*x^2-w^7*x-2*w^6*x^2-w^6*x-w^5*x^2+w^5*x+3*w^4*x+w^3*x+w^2*x-1)/(2*w^8*x^2+2*w^
7*x^2+2*w^6*x^2+w^5*x^2-w^5*x-3*w^4*x-w^3*x-w^2*x+1), -(w^19*x^3+6*w^18*x^3+10*
w^17*x^3+10*w^16*x^3-2*w^15*x^3-3*w^15*x^2-10*w^14*x^3-10*w^14*x^2-12*w^13*x^3-\
7*w^13*x^2-10*w^12*x^3-7*w^11*x^3+8*w^11*x^2-4*w^10*x^3+13*w^10*x^2-w^9*x^3+w^
10*x+10*w^9*x^2+2*w^9*x+10*w^8*x^2+w^8*x+5*w^7*x^2-w^7*x+2*w^6*x^2-5*w^6*x+w^5*
x^2-5*w^5*x-2*w^4*x-w^3*x-w^2*x+1)/(w^16*x^3+6*w^15*x^3+10*w^14*x^3+12*w^13*x^3
+10*w^12*x^3-3*w^12*x^2+7*w^11*x^3-11*w^11*x^2+4*w^10*x^3-13*w^10*x^2+w^9*x^3-\
10*w^9*x^2-10*w^8*x^2-5*w^7*x^2+w^7*x-2*w^6*x^2+5*w^6*x-w^5*x^2+5*w^5*x+2*w^4*x
+w^3*x+w^2*x-1), -(14*w^41*x^6+78*w^40*x^6+246*w^39*x^6+560*w^38*x^6+964*w^37*x
^6-15*w^37*x^5+1276*w^36*x^6-125*w^36*x^5+1260*w^35*x^6-452*w^35*x^5+784*w^34*x
^6-1007*w^34*x^5-38*w^33*x^6-1621*w^33*x^5-904*w^32*x^6-1989*w^32*x^5-1519*w^31
*x^6+14*w^32*x^4-1787*w^31*x^5-1746*w^30*x^6+114*w^31*x^4-912*w^30*x^5-1622*w^
29*x^6+411*w^30*x^4+418*w^29*x^5-1289*w^28*x^6+871*w^29*x^4+1755*w^28*x^5-897*w
^27*x^6+1228*w^28*x^4+2680*w^27*x^5-545*w^26*x^6+1227*w^27*x^4+3012*w^26*x^5-\
283*w^25*x^6-2*w^27*x^3+764*w^26*x^4+2795*w^25*x^5-121*w^24*x^6-23*w^26*x^3-122
*w^25*x^4+2242*w^24*x^5-40*w^23*x^6-109*w^25*x^3-1083*w^24*x^4+1586*w^23*x^5-9*
w^22*x^6-266*w^24*x^3-1764*w^23*x^4+989*w^22*x^5-w^21*x^6-381*w^23*x^3-2071*w^
22*x^4+538*w^21*x^5-348*w^22*x^3-1979*w^21*x^4+250*w^20*x^5-169*w^21*x^3-1621*w
^20*x^4+97*w^19*x^5+146*w^20*x^3-1177*w^19*x^4+30*w^18*x^5+4*w^20*x^2+487*w^19*
x^3-758*w^18*x^4+7*w^17*x^5+27*w^19*x^2+671*w^18*x^3-431*w^17*x^4+w^16*x^5+53*w
^18*x^2+699*w^17*x^3-213*w^16*x^4+49*w^17*x^2+625*w^16*x^3-90*w^15*x^4+32*w^16*
x^2+475*w^15*x^3-31*w^14*x^4-10*w^15*x^2+319*w^14*x^3-9*w^13*x^4-76*w^14*x^2+
184*w^13*x^3-2*w^12*x^4-120*w^13*x^2+94*w^12*x^3-w^13*x-132*w^12*x^2+43*w^11*x^
3-3*w^12*x-104*w^11*x^2+17*w^10*x^3-3*w^11*x-73*w^10*x^2+5*w^9*x^3-w^10*x-49*w^
9*x^2+w^8*x^3+w^9*x-24*w^8*x^2+7*w^8*x-12*w^7*x^2+13*w^7*x-4*w^6*x^2+10*w^6*x-2
*w^5*x^2+7*w^5*x+3*w^4*x+2*w^3*x+w^2*x-1)/(14*w^37*x^6+78*w^36*x^6+246*w^35*x^6
+560*w^34*x^6+992*w^33*x^6-15*w^33*x^5+1432*w^32*x^6-125*w^32*x^5+1737*w^31*x^6
-466*w^31*x^5+1806*w^30*x^6-1085*w^30*x^5+1630*w^29*x^6-1867*w^29*x^5+1289*w^28
*x^6-2603*w^28*x^5+897*w^27*x^6+14*w^28*x^4-3079*w^27*x^5+545*w^26*x^6+114*w^27
*x^4-3158*w^26*x^5+283*w^25*x^6+438*w^26*x^4-2835*w^25*x^5+121*w^24*x^6+1021*w^
25*x^4-2249*w^24*x^5+40*w^23*x^6+1642*w^24*x^4-1586*w^23*x^5+9*w^22*x^6+2060*w^
23*x^4-989*w^22*x^5+w^21*x^6-2*w^23*x^3+2190*w^22*x^4-538*w^21*x^5-23*w^22*x^3+
2018*w^21*x^4-250*w^20*x^5-121*w^21*x^3+1632*w^20*x^4-97*w^19*x^5-338*w^20*x^3+
1177*w^19*x^4-30*w^18*x^5-590*w^19*x^3+758*w^18*x^4-7*w^17*x^5-722*w^18*x^3+431
*w^17*x^4-w^16*x^5-717*w^17*x^3+213*w^16*x^4-629*w^16*x^3+90*w^15*x^4+4*w^16*x^
2-475*w^15*x^3+31*w^14*x^4+31*w^15*x^2-319*w^14*x^3+9*w^13*x^4+85*w^14*x^2-184*
w^13*x^3+2*w^12*x^4+125*w^13*x^2-94*w^12*x^3+132*w^12*x^2-43*w^11*x^3+104*w^11*
x^2-17*w^10*x^3+73*w^10*x^2-5*w^9*x^3+49*w^9*x^2-w^8*x^3-w^9*x+24*w^8*x^2-7*w^8
*x+12*w^7*x^2-13*w^7*x+4*w^6*x^2-10*w^6*x+2*w^5*x^2-7*w^5*x-3*w^4*x-2*w^3*x-w^2
*x+1), -(2*w^80*x^10+54*w^79*x^10+571*w^78*x^10+3581*w^77*x^10+16052*w^76*x^10+
56470*w^75*x^10-16*w^75*x^9+164313*w^74*x^10-347*w^74*x^9+408502*w^73*x^10-3126
*w^73*x^9+886565*w^72*x^10-17654*w^72*x^9+1704120*w^71*x^10-72960*w^71*x^9+
2928406*w^70*x^10-238753*w^70*x^9+4522629*w^69*x^10-648042*w^69*x^9+6286294*w^
68*x^10+68*w^69*x^8-1502952*w^68*x^9+7839878*w^67*x^10+1226*w^68*x^8-3038748*w^
67*x^9+8686668*w^66*x^10+9798*w^67*x^8-5430878*w^66*x^9+8353795*w^65*x^10+49793
*w^66*x^8-8658638*w^65*x^9+6569848*w^64*x^10+186261*w^65*x^8-12376330*w^64*x^9+
3404210*w^63*x^10+553686*w^64*x^8-15865736*w^63*x^9-702730*w^62*x^10+1367712*w^
63*x^8-18132291*w^62*x^9-5044686*w^61*x^10-66*w^63*x^7+2886227*w^62*x^8-\
18155352*w^61*x^9-8852883*w^60*x^10-1056*w^62*x^7+5296572*w^61*x^8-15227698*w^
60*x^9-11515428*w^59*x^10-8243*w^61*x^7+8551581*w^60*x^8-9258039*w^59*x^9-\
12727698*w^58*x^10-41629*w^60*x^7+12227897*w^59*x^8-901839*w^58*x^9-12527311*w^
57*x^10-154566*w^59*x^7+15499406*w^58*x^8+8554222*w^57*x^9-11221536*w^56*x^10-\
452744*w^58*x^7+17290101*w^57*x^8+17525867*w^56*x^9-9254436*w^55*x^10-1090890*w
^57*x^7+16591804*w^56*x^8+24561166*w^55*x^9-7071042*w^54*x^10-2220077*w^56*x^7+
12835237*w^55*x^8+28709038*w^54*x^9-5020521*w^53*x^10+99*w^56*x^6-3883632*w^55*
x^7+6159042*w^54*x^8+29702435*w^53*x^9-3314059*w^52*x^10+1494*w^55*x^6-5905426*
w^54*x^7-2545359*w^53*x^8+27918304*w^52*x^9-2030426*w^51*x^10+10644*w^54*x^6-\
7841857*w^53*x^7-11848198*w^52*x^8+24167378*w^51*x^9-1150226*w^50*x^10+48274*w^
53*x^6-9053019*w^52*x^7-20176858*w^51*x^8+19415786*w^50*x^9-598884*w^49*x^10+
158492*w^52*x^6-8895692*w^51*x^7-26238248*w^50*x^8+14538569*w^49*x^9-284172*w^
48*x^10+405504*w^51*x^6-6972301*w^50*x^7-29319205*w^49*x^8+10166637*w^48*x^9-\
121480*w^47*x^10+844596*w^50*x^6-3320268*w^49*x^7-29380370*w^48*x^8+6640101*w^
47*x^9-46068*w^46*x^10+1471311*w^49*x^6+1550141*w^48*x^7-26947429*w^47*x^8+
4044513*w^46*x^9-15175*w^45*x^10-36*w^49*x^5+2180042*w^48*x^6+6788792*w^47*x^7-\
22876354*w^46*x^8+2290549*w^45*x^9-4216*w^44*x^10-679*w^48*x^5+2764240*w^47*x^6
+11459592*w^46*x^7-18091476*w^45*x^8+1200641*w^44*x^9-946*w^43*x^10-5243*w^47*x
^5+2968874*w^46*x^6+14808887*w^45*x^7-13376951*w^44*x^8+578895*w^43*x^9-160*w^
42*x^10-23645*w^46*x^5+2585128*w^45*x^6+16441405*w^44*x^7-9263332*w^43*x^8+
254705*w^42*x^9-18*w^41*x^10-72820*w^45*x^5+1546006*w^44*x^6+16362427*w^43*x^7-\
6008601*w^42*x^8+101246*w^41*x^9-w^40*x^10-167935*w^44*x^5-27552*w^43*x^6+
14900998*w^42*x^7-3646417*w^41*x^8+35910*w^40*x^9-307361*w^43*x^5-1852818*w^42*
x^6+12561317*w^41*x^7-2065424*w^40*x^8+11188*w^39*x^9-462478*w^42*x^5-3574329*w
^41*x^6+9868256*w^40*x^7-1088076*w^39*x^8+2999*w^38*x^9+3*w^42*x^4-580319*w^41*
x^5-4878803*w^40*x^6+7253690*w^39*x^7-530576*w^38*x^8+671*w^37*x^9+110*w^41*x^4
-599586*w^40*x^5-5582020*w^39*x^6+4999004*w^38*x^7-238023*w^37*x^8+119*w^36*x^9
+1089*w^40*x^4-476080*w^39*x^5-5657332*w^38*x^6+3231817*w^37*x^7-97471*w^36*x^8
+15*w^35*x^9+5316*w^39*x^4-204083*w^38*x^5-5210539*w^37*x^6+1958521*w^36*x^7-\
36068*w^35*x^8+w^34*x^9+16047*w^38*x^4+175756*w^37*x^5-4422238*w^36*x^6+1110374
*w^35*x^7-11903*w^34*x^8+34226*w^37*x^4+585623*w^36*x^5-3487147*w^35*x^6+587132
*w^34*x^7-3441*w^33*x^8+55994*w^36*x^4+938056*w^35*x^5-2567775*w^34*x^6+288353*
w^33*x^7-848*w^32*x^8+73317*w^35*x^4+1167313*w^34*x^5-1770780*w^33*x^6+130817*w
^32*x^7-170*w^31*x^8+77197*w^34*x^4+1246988*w^33*x^5-1145118*w^32*x^6+54440*w^
31*x^7-25*w^30*x^8-5*w^34*x^3+60890*w^33*x^4+1189865*w^32*x^5-694346*w^31*x^6+
20595*w^30*x^7-2*w^29*x^8-76*w^33*x^3+22518*w^32*x^4+1035283*w^31*x^5-394163*w^
30*x^6+6996*w^29*x^7-467*w^32*x^3-32362*w^31*x^4+830962*w^30*x^5-208882*w^29*x^
6+2093*w^28*x^7-1580*w^31*x^3-91400*w^30*x^4+619343*w^29*x^5-102920*w^28*x^6+
533*w^27*x^7-3424*w^30*x^3-140488*w^29*x^4+430570*w^28*x^5-46901*w^27*x^6+108*w
^26*x^7-5236*w^29*x^3-169328*w^28*x^4+279829*w^27*x^5-19640*w^26*x^6+15*w^25*x^
7-6064*w^28*x^3-174768*w^27*x^4+170131*w^26*x^5-7486*w^25*x^6+w^24*x^7-5342*w^
27*x^3-160566*w^26*x^4+96678*w^25*x^5-2558*w^24*x^6-2755*w^26*x^3-133950*w^25*x
^4+51223*w^24*x^5-764*w^23*x^6+1686*w^25*x^3-102636*w^24*x^4+25232*w^23*x^5-190
*w^22*x^6+5*w^25*x^2+7150*w^24*x^3-72753*w^23*x^4+11497*w^22*x^5-36*w^21*x^6+49
*w^24*x^2+12071*w^23*x^3-47875*w^22*x^4+4802*w^21*x^5-4*w^20*x^6+161*w^23*x^2+
15015*w^22*x^3-29266*w^21*x^4+1811*w^20*x^5+251*w^22*x^2+15556*w^21*x^3-16658*w
^20*x^4+606*w^19*x^5+251*w^21*x^2+14109*w^20*x^3-8821*w^19*x^4+173*w^18*x^5+202
*w^20*x^2+11434*w^19*x^3-4330*w^18*x^4+40*w^17*x^5+79*w^19*x^2+8407*w^18*x^3-\
1951*w^17*x^4+6*w^16*x^5-169*w^18*x^2+5660*w^17*x^3-799*w^16*x^4-507*w^17*x^2+
3514*w^16*x^3-294*w^15*x^4-766*w^16*x^2+2015*w^15*x^3-93*w^14*x^4-w^16*x-855*w^
15*x^2+1073*w^14*x^3-24*w^13*x^4-4*w^15*x-784*w^14*x^2+512*w^13*x^3-4*w^12*x^4-\
6*w^14*x-626*w^13*x^2+224*w^12*x^3-4*w^13*x-452*w^12*x^2+90*w^11*x^3-w^12*x-287
*w^11*x^2+31*w^10*x^3+w^11*x-168*w^10*x^2+9*w^9*x^3+9*w^10*x-86*w^9*x^2+w^8*x^3
+25*w^9*x-41*w^8*x^2+29*w^8*x-18*w^7*x^2+21*w^7*x-6*w^6*x^2+14*w^6*x-2*w^5*x^2+
9*w^5*x+5*w^4*x+2*w^3*x+w^2*x-1)/(2*w^75*x^10+54*w^74*x^10+571*w^73*x^10+3581*w
^72*x^10+16052*w^71*x^10+56474*w^70*x^10-16*w^70*x^9+164421*w^69*x^10-347*w^69*
x^9+409644*w^68*x^10-3128*w^68*x^9+893711*w^67*x^10-17708*w^67*x^9+1735906*w^66
*x^10-73531*w^66*x^9+3038748*w^65*x^10-242334*w^65*x^9+4837918*w^64*x^10-664152
*w^64*x^9+7053288*w^63*x^10+68*w^64*x^8-1560470*w^63*x^9+9465707*w^62*x^10+1226
*w^63*x^8-3211479*w^62*x^9+11740647*w^61*x^10+9827*w^62*x^8-5882928*w^61*x^9+
13501838*w^60*x^10+50315*w^61*x^8-9712654*w^60*x^9+14433399*w^59*x^10+190416*w^
60*x^8-14595919*w^59*x^9+14371790*w^58*x^10+574923*w^59*x^8-20122804*w^58*x^9+
13350750*w^57*x^10+1448551*w^58*x^8-25609679*w^57*x^9+11583154*w^56*x^10-66*w^
58*x^7+3134290*w^57*x^8-30232853*w^56*x^9+9391014*w^55*x^10-1056*w^57*x^7+
5940791*w^56*x^8-33229833*w^55*x^9+7114183*w^54*x^10-8292*w^56*x^7+10013705*w^
55*x^8-34102003*w^54*x^9+5031448*w^53*x^10-42501*w^55*x^7+15193317*w^54*x^8-\
32745687*w^53*x^9+3316132*w^52*x^10-161167*w^54*x^7+20957075*w^53*x^8-29465149*
w^52*x^9+2030686*w^51*x^10-484242*w^53*x^7+26497522*w^52*x^8-24869247*w^51*x^9+
1150242*w^50*x^10-1202162*w^52*x^7+30920173*w^51*x^8-19696873*w^50*x^9+598884*w
^49*x^10-2535942*w^51*x^7+33485376*w^50*x^8-14636525*w^49*x^9+284172*w^48*x^10+
99*w^51*x^6-4640515*w^50*x^7+33802950*w^49*x^8-10195797*w^48*x^9+121480*w^47*x^
10+1494*w^50*x^6-7488195*w^49*x^7+31914893*w^48*x^8-6647321*w^47*x^9+46068*w^46
*x^10+10807*w^49*x^6-10801457*w^48*x^7+28249941*w^47*x^8-4045933*w^46*x^9+15175
*w^45*x^10+50377*w^48*x^6-14087418*w^47*x^7+23481005*w^46*x^8-2290749*w^45*x^9+
4216*w^44*x^10+171501*w^47*x^6-16771425*w^46*x^7+18342854*w^45*x^8-1200656*w^44
*x^9+946*w^43*x^10+458007*w^46*x^6-18372802*w^45*x^7+13469478*w^44*x^8-578895*w
^43*x^9+160*w^42*x^10+1002641*w^45*x^6-18641829*w^44*x^7+9293003*w^43*x^8-\
254705*w^42*x^9+18*w^41*x^10+1854385*w^44*x^6-17609200*w^43*x^7+6016683*w^42*x^
8-101246*w^41*x^9+w^40*x^10-36*w^44*x^5+2965975*w^43*x^6-15546676*w^42*x^7+
3648207*w^41*x^8-35910*w^40*x^9-679*w^43*x^5+4180069*w^42*x^6-12865208*w^41*x^7
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7+1088102*w^39*x^8-2999*w^38*x^9-25340*w^41*x^5+6016396*w^40*x^6-7302535*w^39*x
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