01243_01342_02143_02341_03142_03241_12043_12340_13042_13240_23041_23140
Counting sequence:
1, 1, 2, 6, 24, 108, 512, 2506, 12560, 64148, 332704, 1747748, 9280416, 49731768, 268613568, 1460847018, 7992819600, 43965495588, 242989734432, 1348696517964, 7514649244128, 42016005233352, 235665924826176, 1325673785058180, 7477059086539424, 42275419332388168, 239567065205029952, 1360430550201086216, 7740541529962849600, 44121903718663304816, 251926012956167788416, 1440723346709420323050, 8251526397226054378896, 47325506341456085391044, 271786623474630428921632, 1562788803506076123276092, 8996677655300269717462880, 51849710099274003611880232, 299135253656989772968570688, 1727518371379928454124795692, 9985964362150530485633093856, 57776286878192693593012410072, 334566888415810890109628624064, 1938977296357297668690780126072, 11246122791729048828273340522176, 65276702838022040177312854687248, 379162018386459854897967213964416, 2203887896727351931462092857872452, 12818578802907040062728896459099296, 74604385827938481830036016591676968, 434462240601801508475329890307377984, 2531585750986910546600168334851175288, 14759664794912254679344147270042228416, 86098276565704160505129878429889486288, 502502127052964432971614450309457836672, 2934260529558409958200729899476504572104, 17142297742809733369814446663673080838976, 100193989631846794863438089051656145000208, 585881298957241605707816302422627915922560, 3427412198959300374395229820786600381361424, 20058826079181414729753761725433868754829952, 117441395210113950495431812877518683380531424, 687872163841724453951139456406351988547211008, 4030507285692431229515124627225048578233718634, 23625008778897280982203179989975157970298999184, 138528657830353603112437099415657127651658695684, 812564723246756738736447014995906058542838925600, 4767849187430588997060167064242521466517468492444, 27985236389160897737863521028316080227410024056416, 164313510870831784437152863574548534884231700590312, 965053683684004124265974996517414356176349874494784, 5669696529192648956770750786472761652195311574048796, 33319210031880638533346118531197139691350794765717088, 195863118372582883099492463436163691613210954486406200, 1151676232712791061247592012442399710904386521245396928, 6773680872226457523721023267251852796666142168213246488, 39850391241666605844724772639656670444790011733840246720, 234504422853756838917247747013666828721095231919952413648, 1380311960252026234533905517248856496072783427694817258112, 8126592987747720439234773223955537594539386154771072879852, 47856638959472017530990431480339382696406105977645766642400, 281887478810888775481208067097163656208822685984896167665464, 1660759912179625919782323379294456881712523319721615284746176, 9786627447438641209074951322774802915192612274435322325567336, 57683570672143779423382512641302661677397642084593499454417984, 340064982333224833479996003127128079800709441144935651792656496, 2005211958269693399853156628133485927467451178551251126985140096, 11826200085609889873780660499839146735994771144737530364027183800, 69761331545278897919058782352151346381868238971868725790142673088, 411592077809463680288535127338566893823404742420916427669783530224, 2428846822056866792706535049244189739654069228558939325773621531520, 14335483562801876293914111020224695847541584418479628599704196471408, 84625637675796166669772601999607632349398732803958861799548809996672, 499651606454183581127269015671181972775669113720617756349050932170272, 2950575566619383450873896792722924871437695755786574863788787290761472, 17426844619940691203062420740910668586130860741147730301770153055364548, 102944187920369954062827878916073761421914578758564675417624856213823648, 608211320850328169365686702434380699182156515406286277494091470148815080, 3593977426329137610994692434217117322949885631731520586787962875498041664, 21240414835820696095710002540784456876372219653125555025000684553687707544, 125549826043436215314932204120654409881660015237404901275197222335558351808
Generating function in Maple syntax:
(2*x^3-5*x^2-(12*x^2-8*x+1)^(1/2)+5*x+1)/x/(2*x-3)^2
Generating function in latex syntax:
\frac{2 x^{3}-5 x^{2}-\sqrt{12 x^{2}-8 x +1}+5 x +1}{x \left(2 x -3\right)^{2}}
Generating function in sympy syntax:
(2*x**3 - 5*x**2 + 5*x - sqrt(12*x**2 - 8*x + 1) + 1)/(x*(2*x - 3)**2)
Implicit equation for the generating function in Maple syntax:
x*(2*x-3)^2*F(x)^2+(-4*x^3+10*x^2-10*x-2)*F(x)+x^3-2*x^2+3*x+2 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -3\right)^{2} F \! \left(x \right)^{2}+\left(-4 x^{3}+10 x^{2}-10 x -2\right) F \! \left(x \right)+x^{3}-2 x^{2}+3 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 8*(n+2)/(n+4)*a(n)-4/3*(13*n+23)/(n+4)*a(1+n)+2/3*(13*n+35)/(n+4)*a(n+2), n >= 4
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(n +3\right) = \frac{8 \left(n +2\right) a \! \left(n \right)}{n +4}-\frac{4 \left(13 n +23\right) a \! \left(1+n \right)}{3 \left(n +4\right)}+\frac{2 \left(13 n +35\right) a \! \left(n +2\right)}{3 \left(n +4\right)}, \quad n \geq 4
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24257/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[116,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[114,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[14,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[3,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[13,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[53,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[41,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[29,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]+F[26,x,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[21,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]
F[29,x,k[0]] = F[21,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[33,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[21,x,k[0]]*F[24,x,k[0]]
F[33,x,k[0]] = F[21,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[38,x,k[0]]
F[35,x,k[0]] = F[21,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[21,x,k[0]]*F[35,x,k[0]]
F[38,x,k[0]] = F[30,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[21,x,k[0]]*F[38,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[3,x]+F[43,x,k[0]]
F[43,x,k[0]] = F[31,x]+F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[45,x,k[0]] = F[21,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[50,x,k[0]]
F[47,x,k[0]] = F[3,x]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[21,x,k[0]]*F[47,x,k[0]]
F[50,x,k[0]] = F[43,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[21,x,k[0]]*F[50,x,k[0]]
F[53,x,k[0]] = F[111,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[92,x,k[0]]
F[55,x,k[0]] = F[56,x]+F[66,x,k[0]]
F[56,x] = F[57,x]
F[57,x] = F[3,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[1,x]+F[3,x]
F[60,x] = F[56,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[3,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[3,x]
F[65,x] = F[61,x]
F[66,x,k[0]] = F[31,x]+F[67,x,k[0]]+F[84,x,k[0]]
F[67,x,k[0]] = F[3,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[70,x,k[0]]
F[69,x,k[0]] = F[19,x,k[0]]+F[43,x,k[0]]
F[70,x,k[0]] = F[66,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = 2*F[31,x]+F[72,x,k[0]]+F[76,x,k[0]]
F[72,x,k[0]] = F[3,x]*F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[75,x,k[0]]
F[74,x,k[0]] = F[43,x,k[0]]
F[75,x,k[0]] = F[71,x,k[0]]
F[76,x,k[0]] = F[21,x,k[0]]*F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[61,x]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[21,x,k[0]]*F[78,x,k[0]]
F[81,x,k[0]] = F[71,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[21,x,k[0]]*F[81,x,k[0]]
F[84,x,k[0]] = F[21,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[89,x,k[0]]
F[86,x,k[0]] = F[56,x]+F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[21,x,k[0]]*F[86,x,k[0]]
F[89,x,k[0]] = F[66,x,k[0]]+F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[21,x,k[0]]*F[89,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]+F[98,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[3,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]+F[97,x,k[0]]
F[96,x,k[0]] = F[21,x,k[0]]
F[97,x,k[0]] = F[93,x,k[0]]
F[98,x,k[0]] = 2*F[31,x]+F[103,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[3,x]
F[100,x,k[0]] = F[101,x,k[0]]+F[102,x,k[0]]
F[101,x,k[0]] = F[30,x,k[0]]
F[102,x,k[0]] = F[98,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[21,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[108,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[93,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[105,x,k[0]]*F[21,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[98,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[108,x,k[0]]*F[21,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[61,x]+F[71,x,k[0]]
F[113,x,k[0]] = F[12,x,k[0]]*F[3,x]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[21,x,k[0]]*F[23,x,k[0]]*F[7,x,k[0]]
F[116,x] = F[117,x]*F[3,x]
F[117,x] = F[10,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_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{116}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{114}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{3}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{45}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{3}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{3}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{3}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{3}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{3}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{56}\! \left(x \right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{3}\! \left(x \right)
F_{117}\! \left(x \right) = F_{10}\! \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_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_116(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), F_1(x) + F_113(x, k_0) + F_114(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_14(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_3(x))
Eq(F_12(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_53(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_41(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_29(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0) + F_26(x, k_0))
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))
Eq(F_26(x, k_0), F_19(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_21(x, k_0)*F_26(x, k_0))
Eq(F_29(x, k_0), F_21(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_33(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_21(x, k_0)*F_24(x, k_0))
Eq(F_33(x, k_0), F_21(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_38(x, k_0))
Eq(F_35(x, k_0), F_21(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_21(x, k_0)*F_35(x, k_0))
Eq(F_38(x, k_0), F_30(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_21(x, k_0)*F_38(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_3(x) + F_43(x, k_0))
Eq(F_43(x, k_0), F_31(x) + F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_45(x, k_0), F_21(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_50(x, k_0))
Eq(F_47(x, k_0), F_3(x) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_21(x, k_0)*F_47(x, k_0))
Eq(F_50(x, k_0), F_43(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_21(x, k_0)*F_50(x, k_0))
Eq(F_53(x, k_0), F_111(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_92(x, k_0))
Eq(F_55(x, k_0), F_56(x) + F_66(x, k_0))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_3(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_1(x) + F_3(x))
Eq(F_60(x), F_56(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_3(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_3(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x, k_0), F_31(x) + F_67(x, k_0) + F_84(x, k_0))
Eq(F_67(x, k_0), F_3(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_70(x, k_0))
Eq(F_69(x, k_0), F_19(x, k_0) + F_43(x, k_0))
Eq(F_70(x, k_0), F_66(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), 2*F_31(x) + F_72(x, k_0) + F_76(x, k_0))
Eq(F_72(x, k_0), F_3(x)*F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_75(x, k_0))
Eq(F_74(x, k_0), F_43(x, k_0))
Eq(F_75(x, k_0), F_71(x, k_0))
Eq(F_76(x, k_0), F_21(x, k_0)*F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_61(x) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_21(x, k_0)*F_78(x, k_0))
Eq(F_81(x, k_0), F_71(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_21(x, k_0)*F_81(x, k_0))
Eq(F_84(x, k_0), F_21(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_89(x, k_0))
Eq(F_86(x, k_0), F_56(x) + F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_21(x, k_0)*F_86(x, k_0))
Eq(F_89(x, k_0), F_66(x, k_0) + F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_21(x, k_0)*F_89(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0) + F_98(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_3(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0) + F_97(x, k_0))
Eq(F_96(x, k_0), F_21(x, k_0))
Eq(F_97(x, k_0), F_93(x, k_0))
Eq(F_98(x, k_0), F_103(x, k_0) + 2*F_31(x) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_3(x))
Eq(F_100(x, k_0), F_101(x, k_0) + F_102(x, k_0))
Eq(F_101(x, k_0), F_30(x, k_0))
Eq(F_102(x, k_0), F_98(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_21(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_108(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_93(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_105(x, k_0)*F_21(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_98(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_108(x, k_0)*F_21(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_61(x) + F_71(x, k_0))
Eq(F_113(x, k_0), F_12(x, k_0)*F_3(x))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_21(x, k_0)*F_23(x, k_0)*F_7(x, k_0))
Eq(F_116(x), F_117(x)*F_3(x))
Eq(F_117(x), F_10(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "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": "col_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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], 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