0123_0231_1203_3012
Counting sequence:
1, 1, 2, 6, 20, 64, 197, 603, 1883, 6065, 20147, 68666, 238703, 842299, 3006559, 10830323, 39307185, 143566911, 527242584, 1945568949, 7209864278, 26819945170, 100109739291, 374838344494, 1407478680023, 5298663429765, 19995257608712, 75621286311419, 286580606113766, 1088108522343134, 4138699586132741, 15767802125455339, 60165594204933391, 229907734657786025, 879730367885594199, 3370558321939987702, 12929416955979726067, 49653749712499776571, 190895057766004538087, 734653299023810252232, 2830041167135524409159, 10912010647202429287105, 42111350556297985890857, 162651451720784390477622, 628730272177838350471497, 2432219982047342211812109, 9415834518730900070328615, 36476960216986050517026692, 141406558812536797038892207, 548528989729749070710598869, 2129106986250268545224271295, 8268993944937602906287688636, 32133289607236873949862418731, 124938311899387756376494818843, 486032312148164376150567409107, 1891713380290612954481518208898, 7366450675910672569997691574007, 28698981539959406587442206774537, 111859485947656397229496931704275, 436184809772616009587954405005672, 1701583350947947427470805410625591, 6640714311100208597484081940298571, 25926831684072599025863094676971147, 101263203519301044183160097568652191, 395654564634816546674010484099672701, 1546457495117718872372276821971200627, 6046614743615752996229257262233257820, 23650185044169923916190442648298302745, 92533790691457356710282251948275606706, 362164229710606985165991347607957309446, 1417901775868046788584014367211255235847, 5552880213852937457361453247465830764430, 21752960062339768294882050103993623687555, 85239874849749370495917087694257099244521, 334109062214835593049532943803708945634456, 1309940234439746934052496503661694553321987, 5137234297510674097453572587440731881830710, 20152036622050750729015846973373565152932470, 79071016336753158034621560662801449958110481, 310328557734653633224269600870270947629481136, 1218230732915564008337101585235399291413884017, 4783416385990254320416834288095794857629594515, 18786470022982458265881707224647453646864321700, 73798607327147154150796278256347259477049890511, 289964508049299009845459740747333518917746619306, 1139549000592355850320879094458031157073006934422, 4479303796183519203904926309370416867312937128055, 17610647546273543920955293676084043032021053499060, 69250902478301496775835359111876749109177819337871, 272369788519098500560280167489834309440512328510781, 1071455051585739185760972989978590962351154227500362, 4215690425035684811486298343511713959071109049252645, 16589811855600339041139226671575111087894755578072380, 65296593385837111543301456145357643778529141433435836, 257048026963864969418982001677896760055424950256899601, 1012071364348504440705274744009206081859682728739884432, 3985470374869672712952418094064252837257782131502357505, 15697053574493986363777321338592232686150618233463444515, 61833719228095976553025244914158826437428882958305781726, 243612676161691878707838894932429101275834951752509101261, 959931695596324123509422643572780435589093016534517785272
Generating function in Maple syntax:
-1/2*(-1+(1-4*x)^(1/2))/x*(x^5-5*x^4+9*x^3-10*x^2+5*x-1)/(x-1)^5
Generating function in latex syntax:
-\frac{\left(-1+\sqrt{1-4 x}\right) \left(x^{5}-5 x^{4}+9 x^{3}-10 x^{2}+5 x -1\right)}{2 x \left(x -1\right)^{5}}
Generating function in sympy syntax:
(1/2 - sqrt(1 - 4*x)/2)*(x**5 - 5*x**4 + 9*x**3 - 10*x**2 + 5*x - 1)/(x*(x - 1)**5)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^10*F(x)^2-(x^5-5*x^4+9*x^3-10*x^2+5*x-1)*(x-1)^5*F(x)+(x^5-5*x^4+9*x^3-10*x^2+5*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{10} F \! \left(x \right)^{2}-\left(x^{5}-5 x^{4}+9 x^{3}-10 x^{2}+5 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+\left(x^{5}-5 x^{4}+9 x^{3}-10 x^{2}+5 x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 197
a(7) = 603
a(8) = 1883
a(9) = 6065
a(10) = 20147
a(n+7) = 2*(2*n+1)/(n+8)*a(n)-(25*n+38)/(n+8)*a(n+1)+2*(31*n+75)/(n+8)*a(n+2)-2*(45*n+166)/(n+8)*a(n+3)+(368+79*n)/(n+8)*a(n+4)-3*(13*n+74)/(n+8)*a(n+5)+2*(5*n+34)/(n+8)*a(n+6)+1/6*(n+4)*(n+3)*(n+2)/(n+8), n >= 11
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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 197
a \! \left(7\right) = 603
a \! \left(8\right) = 1883
a \! \left(9\right) = 6065
a \! \left(10\right) = 20147
a \! \left(n +7\right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{n +8}-\frac{\left(25 n +38\right) a \! \left(n +1\right)}{n +8}+\frac{2 \left(31 n +75\right) a \! \left(n +2\right)}{n +8}-\frac{2 \left(45 n +166\right) a \! \left(n +3\right)}{n +8}+\frac{\left(368+79 n \right) a \! \left(n +4\right)}{n +8}-\frac{3 \left(13 n +74\right) a \! \left(n +5\right)}{n +8}+\frac{2 \left(5 n +34\right) a \! \left(n +6\right)}{n +8}+\frac{\left(n +4\right) \left(n +3\right) \left(n +2\right)}{6 n +48}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21154/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[22,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[88,x]
F[4,x] = F[22,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[85,x,k[0]]+F[87,x,k[0]]
F[7,x,k[0]] = F[22,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[42,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[35,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x]+F[31,x,k[0]]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[22,x]
F[18,x] = F[19,x]+F[23,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[22,x]
F[22,x] = x
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[22,x]*F[27,x]
F[27,x] = F[20,x]+F[24,x]
F[28,x] = F[22,x]*F[29,x]
F[29,x] = F[20,x]+F[30,x]
F[30,x] = F[28,x]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[14,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[20,x]+F[34,x,k[0]]
F[34,x,k[0]] = F[32,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[37,x,k[0]]
F[36,x,k[0]] = F[20,x]
F[37,x,k[0]] = F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[22,x]*F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[39,x]
F[42,x,k[0]] = F[43,x,k[0]]+F[76,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[49,x,k[0]]
F[44,x,k[0]] = F[20,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[25,x]+F[46,x,k[0]]+F[48,x,k[0]]
F[46,x,k[0]] = F[22,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[12,x,k[0]]+F[45,x,k[0]]
F[48,x,k[0]] = F[14,x,k[0]]*F[44,x,k[0]]
F[49,x,k[0]] = F[50,x]+F[68,x,k[0]]
F[50,x] = F[25,x]+F[51,x]+F[53,x]
F[51,x] = F[22,x]*F[52,x]
F[52,x] = F[16,x]+F[50,x]
F[53,x] = F[22,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[20,x]+F[41,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = F[25,x]+F[58,x]+F[60,x]
F[58,x] = F[22,x]*F[59,x]
F[59,x] = F[20,x]+F[57,x]
F[60,x] = F[22,x]*F[61,x]
F[61,x] = F[20,x]+F[57,x]
F[62,x] = 2*F[25,x]+F[63,x]+F[66,x]
F[63,x] = F[22,x]*F[64,x]
F[64,x] = F[30,x]+F[65,x]
F[65,x] = F[63,x]
F[66,x] = F[22,x]*F[67,x]
F[67,x] = F[41,x]+F[62,x]
F[68,x,k[0]] = 2*F[25,x]+F[69,x,k[0]]+F[71,x,k[0]]
F[69,x,k[0]] = F[22,x]*F[70,x,k[0]]
F[70,x,k[0]] = F[31,x,k[0]]+F[68,x,k[0]]
F[71,x,k[0]] = F[14,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[57,x]+F[73,x,k[0]]
F[73,x,k[0]] = 2*F[25,x]+F[71,x,k[0]]+F[74,x,k[0]]
F[74,x,k[0]] = F[22,x]*F[75,x,k[0]]
F[75,x,k[0]] = F[34,x,k[0]]+F[73,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[78,x,k[0]]
F[77,x,k[0]] = F[24,x]
F[78,x,k[0]] = F[79,x]
F[79,x] = 2*F[25,x]+F[80,x]+F[82,x]
F[80,x] = F[22,x]*F[81,x]
F[81,x] = F[38,x]+F[79,x]
F[82,x] = F[22,x]*F[83,x]
F[83,x] = F[41,x]+F[84,x]
F[84,x] = F[82,x]
F[85,x,k[0]] = F[22,x]*F[86,x,k[0]]
F[86,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[87,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[88,x] = F[22,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[1,x]+F[16,x]
F[92,x] = F[20,x]+F[38,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[20,x]+F[50,x]
F[95,x] = F[24,x]+F[79,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_{22}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{88}\! \left(x \right)
F_{4}\! \left(x \right) = F_{22}\! \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_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{85}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{22}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{22}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{20}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{22}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{22}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{30}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{41}\! \left(x \right)+F_{62}\! \left(x \right)
F_{68}\! \left(x , y\right) = 2 F_{25}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{57}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = 2 F_{25}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{24}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{22}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{38}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{22}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{41}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{82}\! \left(x \right)
F_{85}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{88}\! \left(x \right) = F_{22}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)
F_{95}\! \left(x \right) = F_{24}\! \left(x \right)+F_{79}\! \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_22(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_88(x))
Eq(F_4(x), F_22(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_85(x, k_0) + F_87(x, k_0))
Eq(F_7(x, k_0), F_22(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_42(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_35(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x) + F_31(x, k_0))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_22(x))
Eq(F_18(x), F_19(x) + F_23(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_22(x)*F_27(x))
Eq(F_27(x), F_20(x) + F_24(x))
Eq(F_28(x), F_22(x)*F_29(x))
Eq(F_29(x), F_20(x) + F_30(x))
Eq(F_30(x), F_28(x))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_14(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_20(x) + F_34(x, k_0))
Eq(F_34(x, k_0), F_32(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_37(x, k_0))
Eq(F_36(x, k_0), F_20(x))
Eq(F_37(x, k_0), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_22(x)*F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_39(x))
Eq(F_42(x, k_0), F_43(x, k_0) + F_76(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_49(x, k_0))
Eq(F_44(x, k_0), F_20(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_25(x) + F_46(x, k_0) + F_48(x, k_0))
Eq(F_46(x, k_0), F_22(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_12(x, k_0) + F_45(x, k_0))
Eq(F_48(x, k_0), F_14(x, k_0)*F_44(x, k_0))
Eq(F_49(x, k_0), F_50(x) + F_68(x, k_0))
Eq(F_50(x), F_25(x) + F_51(x) + F_53(x))
Eq(F_51(x), F_22(x)*F_52(x))
Eq(F_52(x), F_16(x) + F_50(x))
Eq(F_53(x), F_22(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_20(x) + F_41(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_25(x) + F_58(x) + F_60(x))
Eq(F_58(x), F_22(x)*F_59(x))
Eq(F_59(x), F_20(x) + F_57(x))
Eq(F_60(x), F_22(x)*F_61(x))
Eq(F_61(x), F_20(x) + F_57(x))
Eq(F_62(x), 2*F_25(x) + F_63(x) + F_66(x))
Eq(F_63(x), F_22(x)*F_64(x))
Eq(F_64(x), F_30(x) + F_65(x))
Eq(F_65(x), F_63(x))
Eq(F_66(x), F_22(x)*F_67(x))
Eq(F_67(x), F_41(x) + F_62(x))
Eq(F_68(x, k_0), 2*F_25(x) + F_69(x, k_0) + F_71(x, k_0))
Eq(F_69(x, k_0), F_22(x)*F_70(x, k_0))
Eq(F_70(x, k_0), F_31(x, k_0) + F_68(x, k_0))
Eq(F_71(x, k_0), F_14(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_57(x) + F_73(x, k_0))
Eq(F_73(x, k_0), 2*F_25(x) + F_71(x, k_0) + F_74(x, k_0))
Eq(F_74(x, k_0), F_22(x)*F_75(x, k_0))
Eq(F_75(x, k_0), F_34(x, k_0) + F_73(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_78(x, k_0))
Eq(F_77(x, k_0), F_24(x))
Eq(F_78(x, k_0), F_79(x))
Eq(F_79(x), 2*F_25(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_22(x)*F_81(x))
Eq(F_81(x), F_38(x) + F_79(x))
Eq(F_82(x), F_22(x)*F_83(x))
Eq(F_83(x), F_41(x) + F_84(x))
Eq(F_84(x), F_82(x))
Eq(F_85(x, k_0), F_22(x)*F_86(x, k_0))
Eq(F_86(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_87(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_88(x), F_22(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_1(x) + F_16(x))
Eq(F_92(x), F_20(x) + F_38(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_20(x) + F_50(x))
Eq(F_95(x), F_24(x) + F_79(x))
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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[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": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[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": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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