02341_02431_04231_20341_20431_24031_40231_42031
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3024, 16600, 93008, 528632, 3036016, 17572504, 102318256, 598547640, 3514448784, 20697555288, 122193434256, 722870024568, 4283626417712, 25420652476696, 151040171643632, 898365403478840, 5348177958053200, 31863910803613144, 189971863888481232, 1133286919217296888, 6764252546801191664, 40392674250900726680, 241304556987475797808, 1442078674261088894392, 8620965459242992376080, 51552719499645670469208, 308363556187027745995536, 1844925997351610277865080, 11040514128223244647741872, 66082315332681015545971224, 395602452858134015816904048, 2368664245230016163201287224, 14184453998834111909135410896, 84953401919612475669843221208, 508865463553505098270332359760, 3048419639120795432530261060344, 18263838744751984221148237695600, 109433748233891951807135352386712, 655766290852357203038419393631664, 3929909229677349335413404998102712, 23553142323911958397797050606771856, 141171045908466019691883604775291736, 846195281443214390393745178475284368, 5072495907584836676143846757313307512, 30408645418131385101355569033294974256, 182303492723355215113858607886127061784, 1092984177330474244850809376310892613616, 6553182839997611945350372280107409661240, 39292430290819285187942984218969756913744, 235603896792641746644069869433142840696792, 1412771389199118808824608205966302545134800, 8471808233740453634181739799956122632974328, 50803564462877744243798187420413990218961392, 304666851830522603623852289945652898768639384, 1827125404106187418035816394588331595629349936, 10957787518356363319009818885466190907713155000, 65718562305105932645369180322825950790201379856, 394151548346267801568845770011979849599700695128, 2364001857242062353838178497044297008731942861840, 14178856783954684034569254135758517129834057920632, 85043850633735642443151606677631618893361776814256, 510096591765192347793484568597225600571930119881752, 3059632562116368706716604461020498509571804507044464, 18352407564040475912906823623647881111086915398551096, 110083780391274563376581340049873379220439265792451024, 660328087321539134260921645196844856377175732773860568, 3960974093435121164326047252963805973149229441701010768, 23760178697855615355864045370589433286625605870322681080, 142528779633083221046919586896356297085073741887412494704, 854988566971519191593963917794935079161142083928533239448, 5128881393158126721665195991626252332221304651025552345776, 30767298187348313536912183601243677376962558664287067111608, 184569605758701753519752665609402847304260420197559135117712, 1107222508145840127243819847625598462938048095345415949858136, 6642220909326942954586042383586679320820573035421290767472784, 39846962158559701663172848892630157707110245472892474900663672, 239045419902874890968339318370587686683834765146280496807693360, 1434064783090131127747700904982965619996062821823843650940632344, 8603201306347830684277691957517485245410459945055045462625791216, 51612419190060572162710999121785450492248208835185467642356645688, 309635693212729945019710652548791500309304339557489660160848534352, 1857592097896450889533454144717424557032837434379133365921767152088, 11144282105031524926952848647532006962419563654180591316911601868240, 66858422176483784611114768334722176920167916867559057510090560760312, 401108918109734422215396370061714106610716252739036482009807355214064, 2406415260265587071910807396569854189159776102871956042054240785303448, 14437127288849578616927488240499986270398055885671481768057999043072304, 86614949956928542305349145083707964597519928355209313523747328841589176, 519644937969720693789264729678148512784351680031994282646887295985655568, 3117613156870598473446554221570652262800110930416843865366027456851542616, 18704209162970334779934534260061686559529733518529960322809373469278543120, 112216830434241572631500237399408730259886268911255906348948021517720844920, 673252685609707100454254897800555228839407623744519745517649516080253417392, 4039239182814913386304312081265634400956794326536522830221403536049067689496
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24173/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[18,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[57,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[18,x]*F[6,x,k[0]]
F[6,x,k[0]] = F[1,x]+F[48,x,k[0]]+F[50,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[18,x]*F[8,x,k[0]]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[16,x,k[0]]+F[46,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[18,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[30,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[18,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[10,x,k[0]]+F[16,x,k[0]]+F[19,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[16,x,k[0]] = F[17,x,k[0]]*F[18,x]
F[17,x,k[0]] = F[15,x,1,k[0]]
F[18,x] = x
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0]]*F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0],k[1]] = (F[23,x,k[0]]*k[0]-F[23,x,k[1]]*k[1])/(-k[1]+k[0])
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]^2*F[21,x,k[0]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[21,x,k[1]]*F[23,x,k[1]]
F[28,x,k[0],k[1]] = F[18,x]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[30,x,k[0],k[1]] = F[21,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,1,k[0],k[1]]
F[32,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[1],k[2]]+F[28,x,k[1],k[2]]+F[33,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[37,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[32,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = F[35,x,k[0]*k[1],k[1],k[2]]
F[35,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[36,x,k[0],k[1],k[2]]
F[36,x,k[0],k[1],k[2]] = (-F[32,x,1,k[1],k[2]]*k[1]+F[32,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[38,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1],k[2]] = (F[39,x,k[0]*k[1],k[2]]*k[0]-F[39,x,k[1],k[2]])/(-1+k[0])
F[39,x,k[0],k[1]] = (-F[40,x,1,k[1]]*k[1]+F[40,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[40,x,k[0],k[1]] = F[1,x]+F[41,x,k[1]]+F[42,x,k[1]]+F[43,x,k[0],k[1]]+F[44,x,k[0],k[1]]
F[41,x,k[0]] = F[17,x,k[0]]*F[18,x]
F[42,x,k[0]] = F[11,x,k[0]]*F[18,x]
F[43,x,k[0],k[1]] = F[21,x,k[1]]*F[40,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[45,x,k[0]*k[1],k[1]]
F[45,x,k[0],k[1]] = F[21,x,k[1]]*F[39,x,k[0],k[1]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[21,x,k[0]]*F[23,x,k[0]]*F[9,x,k[0]]
F[48,x,k[0]] = F[18,x]*F[49,x,k[0]]
F[49,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[50,x,k[0]] = F[21,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,1,k[0]]
F[52,x,k[0],k[1]] = F[53,x,k[0]*k[1],k[1]]
F[53,x,k[0],k[1]] = F[1,x]+F[48,x,k[1]]+F[54,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[7,x,k[1]]
F[54,x,k[0],k[1]] = F[21,x,k[0]]*F[53,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[21,x,k[1]]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = (-F[52,x,1,k[1]]*k[1]+F[52,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[57,x] = F[18,x]*F[58,x]
F[58,x] = F[9,x,1]
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_{18}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{57}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{18}\! \left(x \right) F_{6}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{48}\! \left(x , y_{0}\right)+F_{50}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{18}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = \frac{y_{0} F_{9}\! \left(x , y_{0}\right)-F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{18}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{18}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{15}\! \left(x , y_{0}, y_{1}\right)-F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{16}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{18}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{15}\! \left(x , 1, y_{0}\right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = y_{0} x
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{23}\! \left(x , y_{0}\right)-y_{1} F_{23}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)^{2} F_{21}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x \right) F_{29}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}, y_{1}\right)-F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , 1, y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{35}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{32}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{32}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{39}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}-F_{39}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{40}\! \left(x , 1, y_{1}\right)+y_{0} F_{40}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y_{1}\right)+F_{42}\! \left(x , y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{18}\! \left(x \right)
F_{42}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{18}\! \left(x \right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{45}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{39}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{18}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = \frac{y_{0} F_{6}\! \left(x , y_{0}\right)-F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{50}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{52}\! \left(x , 1, y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{48}\! \left(x , y_{1}\right)+F_{54}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{52}\! \left(x , 1, y_{1}\right)+y_{0} F_{52}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{9}\! \left(x , 1\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_18(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_57(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_18(x)*F_6(x, k_0))
Eq(F_6(x, k_0), F_1(x) + F_48(x, k_0) + F_50(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_18(x)*F_8(x, k_0))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_16(x, k_0) + F_46(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_18(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_28(x, k_0, k_1) + F_30(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_18(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_10(x, k_0) + F_16(x, k_0) + F_19(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_16(x, k_0), F_17(x, k_0)*F_18(x))
Eq(F_17(x, k_0), F_15(x, 1, k_0))
Eq(F_18(x), x)
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0)*F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0) + k_1*F_23(x, k_1))/(-k_0 + k_1))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_21(x, k_0)*F_23(x, k_0)**2)
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_15(x, k_0, k_1)*F_21(x, k_1)*F_23(x, k_1))
Eq(F_28(x, k_0, k_1), F_18(x)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_30(x, k_0, k_1), F_21(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, 1, k_0, k_1))
Eq(F_32(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_1, k_2) + F_28(x, k_1, k_2) + F_33(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_37(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_21(x, k_1)*F_32(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), F_35(x, k_0*k_1, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2), F_21(x, k_1)*F_36(x, k_0, k_1, k_2))
Eq(F_36(x, k_0, k_1, k_2), (-k_0*F_32(x, k_0/k_1, k_1, k_2) + k_1*F_32(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1, k_2), F_21(x, k_2)*F_38(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1, k_2), (-k_0*k_1*F_39(x, k_0*k_1, k_2) + k_1*F_39(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_39(x, k_0, k_1), (-k_0*F_40(x, k_0/k_1, k_1) + k_1*F_40(x, 1, k_1))/(-k_0 + k_1))
Eq(F_40(x, k_0, k_1), F_1(x) + F_41(x, k_1) + F_42(x, k_1) + F_43(x, k_0, k_1) + F_44(x, k_0, k_1))
Eq(F_41(x, k_0), F_17(x, k_0)*F_18(x))
Eq(F_42(x, k_0), F_11(x, k_0)*F_18(x))
Eq(F_43(x, k_0, k_1), F_21(x, k_1)*F_40(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_45(x, k_0*k_1, k_1))
Eq(F_45(x, k_0, k_1), F_21(x, k_1)*F_39(x, k_0, k_1))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_21(x, k_0)*F_23(x, k_0)*F_9(x, k_0))
Eq(F_48(x, k_0), F_18(x)*F_49(x, k_0))
Eq(F_49(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_50(x, k_0), F_21(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, 1, k_0))
Eq(F_52(x, k_0, k_1), F_53(x, k_0*k_1, k_1))
Eq(F_53(x, k_0, k_1), F_1(x) + F_48(x, k_1) + F_54(x, k_0, k_1) + F_55(x, k_0, k_1) + F_7(x, k_1))
Eq(F_54(x, k_0, k_1), F_21(x, k_0)*F_53(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_21(x, k_1)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (-k_0*F_52(x, k_0/k_1, k_1) + k_1*F_52(x, 1, k_1))/(-k_0 + k_1))
Eq(F_57(x), F_18(x)*F_58(x))
Eq(F_58(x), F_9(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_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, 3, 4, 1], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "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]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "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]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "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], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "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], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "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], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 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