02413_02431_04213_04231_20413_20431

Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3300, 18992, 112472, 681120, 4199776, 26281984, 166514824, 1066051504, 6886134512, 44824664000, 293747699616, 1936404214016, 12831857491456, 85429891994112, 571148926488512, 3832928021966720, 25810774536839552, 174352459643351552, 1181126059357084416, 8022396954733405184, 54621330681733827584, 372727359526842318848, 2548710026228555123328, 17461698037446599762688, 119848493837126644700928, 823962617783893720771584, 5673680841894459254661632, 39125750969021067857698816, 270185823761533312775483392, 1868226590807283799968702464, 12933963983111939240952955904, 89647766830517889525763827712, 622051024721062621090913765376, 4320821589260884418574622187520, 30042593927035619511394828996608, 209082640612359636906965211168768, 1456425283428767530243766160834560, 10153826869838395024880543127175168, 70847659122257337758647951263387648, 494720051993653387831829800864899072, 3457139325143024493312259304211308544, 24175957155247791404558898714779418624, 169179152855110457314445797253016207360, 1184661143218738136925337213356853297152, 8300687613506903912540777680733275160576, 58196358095928090387966552627658432446464, 408252798663380776427720703960544180666368, 2865527339288906577989482653984095246680064, 20123934773183305844546202345391678023204864, 141398772936877893008319458135213121036615680, 994018975169391017401740903131409659783938048, 6991209781523424200982625771995184085835710464, 49193910763760369841290249980248267747099148288, 346309834113979416579207597583863778983033176064, 2438968618945416854926133811738743421497132875776, 17184198912908818869800069061567626593564297986048, 121123424750230137894543597784250614788081491312640, 854077205267458225889088066678651719997458628739072, 6024637087161285838150390156264463160801815969267712, 42513249785550036711645180303936152291399959287169024, 300104487031649235635756422184097622469778851060776960, 2119194324056696523969037444998785295855822426200866816, 14969756275438107593956848265783995367926424997809356800, 105779149816164859154154403396241251040722484353489698816, 747692001124959975544465899278737416154639192538858651648, 5286628773962401123268928713923116947145940269854690902016, 37390784489872578314054771085814422709780198700158425235456, 264530916727329033836130904832839187105946640665527929798656, 1872022045068460372491669094820333996169431992169223013007360, 13251494010695315794786002306928630091159265734631354722680832, 93828533416117469187628549007308863108544107732014679628709888, 664535470784941366883734770556637688649569001639569531556855808, 4707730979140646380723770418866017261060301618058685532189229056, 33358961825584832714380788341528980662530744976977593665591443456, 236438463329077349086480832146938041819879545725267141268820983808, 1676200004248604661921210564472883365424778841986415623176995209216, 11885929369754874931180342458014427178108867474268074708679513866240, 84301952566059111651175844198436538878374129976944018399990074310656, 598049280284657852462571222044557674267919172556049723902525070901248, 4243545981752983283610654869444407390086584910068012821459683625664512, 30116970652567089736089217467223585842607869372601388539241533422960640, 213787347244829414463724643424799341099498336562932214147953569711521792, 1517885557147417829795710053507855151730300392987540291643726616128913408, 10779048429869665510783541843586046857072984678712444841555620048333176832, 76560417752810118870729205888889278694542305086229622148582144069999788032, 543887174267679836874909492754423648476807923356440394590719518042644021248, 3864490351434462860171830349038858327302825609939000737794248481806510718976, 27463306005280896279302015151734924084055884129991319941950058400420921868288, 195204097954831658653663028107706146534456095613281425746894954226902246621184, 1387710808628825244122900048953520485048590140076977173408814112967207797391360, 9866914997695841486819949418657461302780844870980402662481777821515846044876800, 70167285628426281977078988774039466614284689666636652164029641885595019404902400, 499065311426165204974168899652063667803425956852248160360515397001933929385558016, 3550161413265281028458423666992972996606187936184130177239417321041772869134057472

Implicit equation for the generating function in Maple syntax:
2*x^3*F(x)^4+(-6*x^2+2*x-1)*F(x)^3+(6*x^2-x+3)*F(x)^2+(-4*x-3)*F(x)+3*x+1 = 0

Implicit equation for the generating function in latex syntax:
2 x^{3} F \! \left(x \right)^{4}+\left(-6 x^{2}+2 x -1\right) F \! \left(x \right)^{3}+\left(6 x^{2}-x +3\right) F \! \left(x \right)^{2}+\left(-4 x -3\right) F \! \left(x \right)+3 x +1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(6) = 596
a(7) = 3300
a(8) = 18992
a(9) = 112472
a(10) = 681120
a(11) = 4199776
a(n+12) = 1096416*(2*n+3)*(2*n+1)*(n+1)/(n+11)/(n+10)/(n+15)*a(n)-11664/5*(2*n+3)*(2183*n^2+9069*n+8560)/(n+11)/(n+10)/(n+15)*a(n+1)+324*(32445*n^3+265710*n^2+695087*n+588862)/(n+11)/(n+10)/(n+15)*a(n+2)-108/5*(293846*n^3+3073815*n^2+10173367*n+10830410)/(n+11)/(n+10)/(n+15)*a(n+3)+18/5*(681285*n^3+8319960*n^2+30995799*n+35324932)/(n+11)/(n+10)/(n+15)*a(n+4)-6/5*(492480*n^3+6268605*n^2+20734897*n+10942692)/(n+11)/(n+10)/(n+15)*a(n+5)+1/5*(271697*n^3+1162164*n^2-25389047*n-128827194)/(n+11)/(n+10)/(n+15)*a(n+6)+3/5*(36422*n^3+1120647*n^2+10936461*n+33591370)/(n+11)/(n+10)/(n+15)*a(n+7)-1/5*(58220*n^3+1588185*n^2+14306551*n+42445860)/(n+11)/(n+10)/(n+15)*a(n+8)+6/5*(2337*n^3+66743*n^2+626529*n+1938604)/(n+11)/(n+10)/(n+15)*a(n+9)-3/10*(1309*n^3+40272*n^2+406191*n+1348028)/(n+11)/(n+10)/(n+15)*a(n+10)+2/5*(76*n^2+1772*n+9927)/(n+15)/(n+11)*a(n+11), n >= 12

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 24
a \! \left(5\right) = 114
a \! \left(6\right) = 596
a \! \left(7\right) = 3300
a \! \left(8\right) = 18992
a \! \left(9\right) = 112472
a \! \left(10\right) = 681120
a \! \left(11\right) = 4199776
a \! \left(n +12\right) = \frac{1096416 \left(2 n +3\right) \left(2 n +1\right) \left(n +1\right) a \! \left(n \right)}{\left(n +11\right) \left(n +10\right) \left(n +15\right)}-\frac{11664 \left(2 n +3\right) \left(2183 n^{2}+9069 n +8560\right) a \! \left(n +1\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{324 \left(32445 n^{3}+265710 n^{2}+695087 n +588862\right) a \! \left(n +2\right)}{\left(n +11\right) \left(n +10\right) \left(n +15\right)}-\frac{108 \left(293846 n^{3}+3073815 n^{2}+10173367 n +10830410\right) a \! \left(n +3\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{18 \left(681285 n^{3}+8319960 n^{2}+30995799 n +35324932\right) a \! \left(n +4\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}-\frac{6 \left(492480 n^{3}+6268605 n^{2}+20734897 n +10942692\right) a \! \left(n +5\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{\left(271697 n^{3}+1162164 n^{2}-25389047 n -128827194\right) a \! \left(n +6\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{3 \left(36422 n^{3}+1120647 n^{2}+10936461 n +33591370\right) a \! \left(n +7\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}-\frac{\left(58220 n^{3}+1588185 n^{2}+14306551 n +42445860\right) a \! \left(n +8\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{6 \left(2337 n^{3}+66743 n^{2}+626529 n +1938604\right) a \! \left(n +9\right)}{5 \left(n +11\right) \left(n +10\right) \left(n +15\right)}-\frac{3 \left(1309 n^{3}+40272 n^{2}+406191 n +1348028\right) a \! \left(n +10\right)}{10 \left(n +11\right) \left(n +10\right) \left(n +15\right)}+\frac{2 \left(76 n^{2}+1772 n +9927\right) a \! \left(n +11\right)}{5 \left(n +15\right) \left(n +11\right)}, \quad n \geq 12

Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24110/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[23,x]
F[11,x] = 1/F[23,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[23,x]*F[24,x]
F[17,x] = 1/F[23,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[8,x]+F[20,x]
F[20,x] = 1/F[23,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[0,x]+F[4,x]
F[23,x] = x
F[24,x] = F[2,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = 1/F[23,x]/F[35,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[23,x]*F[30,x]*F[38,x]
F[30,x] = F[31,x]+F[33,x]
F[31,x] = 1/F[23,x]*F[32,x]
F[32,x] = F[2,x]
F[33,x] = F[34,x]
F[34,x] = F[23,x]*F[35,x]*F[37,x]
F[35,x] = F[30,x]+F[36,x]
F[36,x] = F[33,x]
F[37,x] = F[0,x]+F[25,x]
F[38,x] = 1/F[23,x]/F[30,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]+F[77,x]
F[41,x] = -F[76,x]+F[42,x]
F[42,x] = -F[48,x]+F[43,x]
F[43,x] = 1/F[23,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[0,x]+F[46,x]
F[46,x] = 1/F[23,x]*F[47,x]
F[47,x] = F[2,x]
F[48,x] = F[49,x]+F[71,x]
F[49,x] = F[0,x]*F[50,x]
F[50,x] = -F[53,x]+F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[2,x]
F[53,x] = F[1,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[23,x]*F[56,x]
F[56,x] = F[53,x]+F[57,x]
F[57,x] = F[58,x]+F[63,x]
F[58,x] = F[59,x]
F[59,x] = F[23,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[1,x]+F[58,x]
F[62,x] = F[58,x]
F[63,x] = F[64,x]+F[65,x]+F[69,x]
F[64,x] = 0
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[54,x]+F[63,x]
F[68,x] = F[63,x]
F[69,x] = F[23,x]*F[70,x]
F[70,x] = F[57,x]
F[71,x] = F[72,x]
F[72,x] = F[23,x]*F[38,x]*F[73,x]
F[73,x] = 1/F[23,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = -F[2,x]+F[50,x]
F[76,x] = F[0,x]*F[53,x]
F[77,x] = F[78,x]
F[78,x] = F[23,x]*F[38,x]*F[79,x]
F[79,x] = -F[80,x]+F[30,x]
F[80,x] = F[81,x]+F[96,x]
F[81,x] = F[1,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[23,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[1,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[23,x]*F[85,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[90,x]
F[90,x] = F[23,x]*F[91,x]
F[91,x] = F[1,x]+F[89,x]
F[92,x] = F[64,x]+F[93,x]+F[95,x]
F[93,x] = F[23,x]*F[94,x]
F[94,x] = F[86,x]+F[92,x]
F[95,x] = F[23,x]*F[88,x]
F[96,x] = F[54,x]+F[97,x]
F[97,x] = F[114,x]+F[64,x]+F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[82,x]+F[97,x]
F[101,x] = F[102,x]+F[107,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[23,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[102,x]+F[82,x]
F[106,x] = F[102,x]
F[107,x] = 2*F[64,x]+F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[23,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[107,x]+F[97,x]
F[111,x] = F[107,x]
F[112,x] = F[113,x]*F[23,x]
F[113,x] = F[101,x]
F[114,x] = F[115,x]*F[23,x]
F[115,x] = F[116,x]+F[121,x]
F[116,x] = F[117,x]+F[86,x]
F[117,x] = F[118,x]+F[120,x]+F[64,x]
F[118,x] = F[119,x]*F[23,x]
F[119,x] = F[117,x]+F[86,x]
F[120,x] = F[116,x]*F[23,x]
F[121,x] = F[122,x]+F[127,x]
F[122,x] = F[123,x]+F[125,x]+F[64,x]
F[123,x] = F[124,x]*F[23,x]
F[124,x] = F[122,x]+F[89,x]
F[125,x] = F[126,x]*F[23,x]
F[126,x] = F[122,x]+F[86,x]
F[127,x] = F[128,x]+F[130,x]+F[132,x]+F[64,x]
F[128,x] = F[129,x]*F[23,x]
F[129,x] = F[127,x]+F[92,x]
F[130,x] = F[131,x]*F[23,x]
F[131,x] = F[117,x]+F[127,x]
F[132,x] = F[121,x]*F[23,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{23}\! \left(x \right) F_{35}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right) F_{38}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right) F_{35}\! \left(x \right) F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{23}\! \left(x \right) F_{30}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{77}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{71}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)
F_{53}\! \left(x \right) = F_{1}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{23}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{1}\! \left(x \right)+F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{64}\! \left(x \right) = 0
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{63}\! \left(x \right)
F_{69}\! \left(x \right) = F_{23}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{57}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{76}\! \left(x \right) = F_{0}\! \left(x \right) F_{53}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{30}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{96}\! \left(x \right)
F_{81}\! \left(x \right) = F_{1}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{23}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{23}\! \left(x \right) F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{23}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{64}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{23}\! \left(x \right) F_{88}\! \left(x \right)
F_{96}\! \left(x \right) = F_{54}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{114}\! \left(x \right)+F_{64}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{82}\! \left(x \right)+F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{107}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{23}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)+F_{82}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{64}\! \left(x \right)+F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{23}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{97}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{101}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{23}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{121}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{86}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{120}\! \left(x \right)+F_{64}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{117}\! \left(x \right)+F_{86}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right) F_{23}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{127}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)+F_{64}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{23}\! \left(x \right)
F_{124}\! \left(x \right) = F_{122}\! \left(x \right)+F_{89}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{23}\! \left(x \right)
F_{126}\! \left(x \right) = F_{122}\! \left(x \right)+F_{86}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{64}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{23}\! \left(x \right)
F_{129}\! \left(x \right) = F_{127}\! \left(x \right)+F_{92}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{23}\! \left(x \right)
F_{131}\! \left(x \right) = F_{117}\! \left(x \right)+F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right) F_{23}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_23(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_23(x)*F_24(x))
Eq(F_17(x), F_18(x)/F_23(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) - F_8(x))
Eq(F_20(x), F_21(x)/F_23(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), -F_0(x) + F_4(x))
Eq(F_23(x), x)
Eq(F_24(x), F_2(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_28(x)/(F_23(x)*F_35(x)))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_23(x)*F_30(x)*F_38(x))
Eq(F_30(x), F_31(x) + F_33(x))
Eq(F_31(x), F_32(x)/F_23(x))
Eq(F_32(x), F_2(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_23(x)*F_35(x)*F_37(x))
Eq(F_35(x), F_30(x) + F_36(x))
Eq(F_36(x), F_33(x))
Eq(F_37(x), F_0(x) + F_25(x))
Eq(F_38(x), F_39(x)/(F_23(x)*F_30(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x) + F_77(x))
Eq(F_41(x), F_42(x) - F_76(x))
Eq(F_42(x), F_43(x) - F_48(x))
Eq(F_43(x), F_44(x)/F_23(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), -F_0(x) + F_46(x))
Eq(F_46(x), F_47(x)/F_23(x))
Eq(F_47(x), F_2(x))
Eq(F_48(x), F_49(x) + F_71(x))
Eq(F_49(x), F_0(x)*F_50(x))
Eq(F_50(x), F_51(x) - F_53(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_2(x))
Eq(F_53(x), F_1(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_23(x)*F_56(x))
Eq(F_56(x), F_53(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_63(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_23(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_1(x) + F_58(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_64(x) + F_65(x) + F_69(x))
Eq(F_64(x), 0)
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_54(x) + F_63(x))
Eq(F_68(x), F_63(x))
Eq(F_69(x), F_23(x)*F_70(x))
Eq(F_70(x), F_57(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_23(x)*F_38(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_23(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), -F_2(x) + F_50(x))
Eq(F_76(x), F_0(x)*F_53(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_23(x)*F_38(x)*F_79(x))
Eq(F_79(x), F_30(x) - F_80(x))
Eq(F_80(x), F_81(x) + F_96(x))
Eq(F_81(x), F_1(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_23(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_1(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_23(x)*F_85(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_23(x)*F_91(x))
Eq(F_91(x), F_1(x) + F_89(x))
Eq(F_92(x), F_64(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_23(x)*F_94(x))
Eq(F_94(x), F_86(x) + F_92(x))
Eq(F_95(x), F_23(x)*F_88(x))
Eq(F_96(x), F_54(x) + F_97(x))
Eq(F_97(x), F_114(x) + F_64(x) + F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_82(x) + F_97(x))
Eq(F_101(x), F_102(x) + F_107(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_23(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_102(x) + F_82(x))
Eq(F_106(x), F_102(x))
Eq(F_107(x), F_108(x) + F_112(x) + 2*F_64(x))
Eq(F_108(x), F_109(x)*F_23(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_107(x) + F_97(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), F_113(x)*F_23(x))
Eq(F_113(x), F_101(x))
Eq(F_114(x), F_115(x)*F_23(x))
Eq(F_115(x), F_116(x) + F_121(x))
Eq(F_116(x), F_117(x) + F_86(x))
Eq(F_117(x), F_118(x) + F_120(x) + F_64(x))
Eq(F_118(x), F_119(x)*F_23(x))
Eq(F_119(x), F_117(x) + F_86(x))
Eq(F_120(x), F_116(x)*F_23(x))
Eq(F_121(x), F_122(x) + F_127(x))
Eq(F_122(x), F_123(x) + F_125(x) + F_64(x))
Eq(F_123(x), F_124(x)*F_23(x))
Eq(F_124(x), F_122(x) + F_89(x))
Eq(F_125(x), F_126(x)*F_23(x))
Eq(F_126(x), F_122(x) + F_86(x))
Eq(F_127(x), F_128(x) + F_130(x) + F_132(x) + F_64(x))
Eq(F_128(x), F_129(x)*F_23(x))
Eq(F_129(x), F_127(x) + F_92(x))
Eq(F_130(x), F_131(x)*F_23(x))
Eq(F_131(x), F_117(x) + F_127(x))
Eq(F_132(x), F_121(x)*F_23(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], 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