0132_0231_2031_3102
Counting sequence:
1, 1, 2, 6, 20, 64, 194, 568, 1634, 4664, 13270, 37708, 107098, 304120, 863526, 2451844, 6961538, 19765856, 56120990, 159343644, 452422362, 1284556888, 3647225430, 10355518932, 29402287826, 83481526480, 237027992526, 672990439884, 1910812842442, 5425345595336, 15404111891398, 43736690869188, 124181007101890, 352585488713664, 1001091308185534, 2842385292091324, 8070346913050554, 22914029100208056, 65059499332812726, 184722574756519860, 524480359895244722, 1489150139220524976, 4228124266814160814, 12004857230165032876, 34085232131844538282, 96777748140346343336, 274779778494337286054, 780178585679652847524, 2215150725021954932642, 6289448114357882912672, 17857546728703017615262, 50702695907424448675740, 143959492943601490067354, 408742281602114200797080, 1160536546448899740270486, 3295096045274345138028436, 9355722558506009992626066, 26563579145824458898931600, 75421618439822485901279118, 214143602293004127994642316, 608015093704375486171316106, 1726329202525130404509253512, 4901543639869027929341034374, 13916887936784341071669755780, 39514035592711513378333392770, 112191677903446745085336616832, 318544345116509608971352407934, 904438740037674482300729950076, 2567960935491552983488183402362, 7291177472048533222692518625144, 20701743626303269921418800791414, 58778186488002052761881495469940, 166888126390892197807235815964530, 473843246864167120024254883561328, 1345376854869103794391839261327214, 3819910684801531093084809142992748, 10845821813458043434820389293784938, 30794398224364256955725999125823336, 87434127013227916269792057614139238, 248250558782370724125905012540833636, 704854523525299745335903817958424418, 2001284112998171917379579336898641760, 5682219475456230136426512100842536798, 16133450496882832366859538691692429148, 45807492311702752756491265037196853082, 130060606210192141831379929583702769496, 369279356587723221033273735569408524118, 1048489986133529822320557754017216724820, 2976963730603610688811895932958638341970, 8452453691055769908031900186904503517008, 23998939814075696521521132523817894149966, 68139871953286927831580721213570839215948, 193468635938956465056302155132820787298122, 549312935570829541941928000724635580628808, 1559656942434066163205664824794400851754822, 4428313299330859415167551606544702659100484, 12573251298728832091731403128450478390640450, 35699065882460023032666735737211904629669696, 101359884933586482594076433648135110274318142, 287789778801963502429101597900593779359874876, 817117707238428125405434128484258485601566522
Generating function in Maple syntax:
-(4*x^4-7*x^3+9*x^2-5*x+1)/(2*x^3-4*x^2+4*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{4 x^{4}-7 x^{3}+9 x^{2}-5 x +1}{\left(2 x^{3}-4 x^{2}+4 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-4*x**4 + 7*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**2*(2*x**3 - 4*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x^3-4*x^2+4*x-1)*(x-1)^2*F(x)+4*x^4-7*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{3}-4 x^{2}+4 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+4 x^{4}-7 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
1/4224*(-352*((-6/11*I+2/11*3^(1/2))*11^(1/2)+I*3^(1/2)-1)*2^(1/3)*(13+3*11^(1/2)*3^(1/2))^(1/3)-1408-55*((21/55*I+7/55*3^(1/2))*11^(1/2)+I*3^(1/2)+1)*2^(2/3)*(13+3*11^(1/2)*3^(1/2))^(2/3))*(13/384*2^(2/3)*((I-3/13*11^(1/2))*3^(1/2)-9/13*I*11^(1/2)+1)*(13+3*11^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(26+6*11^(1/2)*3^(1/2))^(1/3)+1/12*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/4224*(352*((-6/11*I-2/11*3^(1/2))*11^(1/2)+I*3^(1/2)+1)*2^(1/3)*(13+3*11^(1/2)*3^(1/2))^(1/3)-1408+55*((21/55*I-7/55*3^(1/2))*11^(1/2)+I*3^(1/2)-1)*2^(2/3)*(13+3*11^(1/2)*3^(1/2))^(2/3))*(-13/384*2^(2/3)*((I+3/13*11^(1/2))*3^(1/2)-9/13*I*11^(1/2)-1)*(13+3*11^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(26+6*11^(1/2)*3^(1/2))^(1/3)+1/12*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/4224*((128*2^(1/3)*11^(1/2)*3^(1/2)-704*2^(1/3))*(13+3*11^(1/2)*3^(1/2))^(1/3)-1408+(14*11^(1/2)*3^(1/2)*2^(2/3)+110*2^(2/3))*(13+3*11^(1/2)*3^(1/2))^(2/3))*(1/192*2^(2/3)*(3*11^(1/2)*3^(1/2)-13)*(13+3*11^(1/2)*3^(1/2))^(2/3)-1/6*(26+6*11^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)-2*n+2
Explicit closed form in latex syntax:
\frac{\left(-352 \left(\left(-\frac{6 \,\mathrm{I}}{11}+\frac{2 \sqrt{3}}{11}\right) \sqrt{11}+\mathrm{I} \sqrt{3}-1\right) 2^{\frac{1}{3}} \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-1408-55 \left(\left(\frac{21 \,\mathrm{I}}{55}+\frac{7 \sqrt{3}}{55}\right) \sqrt{11}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{2}{3}} \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{13 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{3 \sqrt{11}}{13}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{11}}{13}+1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}-\frac{\mathrm{I} \sqrt{3}\, \left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{4224}+\frac{\left(352 \left(\left(-\frac{6 \,\mathrm{I}}{11}-\frac{2 \sqrt{3}}{11}\right) \sqrt{11}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{1}{3}} \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-1408+55 \left(\left(\frac{21 \,\mathrm{I}}{55}-\frac{7 \sqrt{3}}{55}\right) \sqrt{11}+\mathrm{I} \sqrt{3}-1\right) 2^{\frac{2}{3}} \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{13 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{11}}{13}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{11}}{13}-1\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}+\frac{\mathrm{I} \sqrt{3}\, \left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{4224}+\frac{\left(\left(128 \,2^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-704 \,2^{\frac{1}{3}}\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-1408+\left(14 \sqrt{11}\, \sqrt{3}\, 2^{\frac{2}{3}}+110 \,2^{\frac{2}{3}}\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{2}{3}} \left(3 \sqrt{11}\, \sqrt{3}-13\right) \left(13+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{192}-\frac{\left(26+6 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{4224}-2 n +2
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+3) = 2*a(n)-4*a(n+1)+4*a(n+2)+2*n, n >= 5
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(n +3\right) = 2 a \! \left(n \right)-4 a \! \left(n +1\right)+4 a \! \left(n +2\right)+2 n, \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15382/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[25,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[11,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[4,x]
F[24,x] = F[18,x]
F[25,x] = F[26,x]+F[38,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[14,x]
F[30,x] = F[26,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[26,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]*F[4,x]
F[37,x] = F[31,x]
F[38,x] = F[39,x]+F[40,x]+F[60,x]
F[39,x] = 0
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[43,x]+F[7,x]
F[43,x] = F[19,x]
F[44,x] = F[38,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[59,x]
F[48,x] = F[49,x]+F[57,x]
F[49,x] = F[39,x]+F[50,x]+F[55,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[11,x]+F[18,x]
F[53,x] = F[49,x]+F[54,x]
F[54,x] = F[46,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[26,x]+F[49,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[48,x]
F[59,x] = F[54,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[56,x]+F[62,x]
F[62,x] = F[63,x]+F[80,x]
F[63,x] = F[39,x]+F[64,x]+F[77,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[14,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[21,x]
F[70,x] = F[31,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[35,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[74,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[34,x]+F[79,x]
F[79,x] = F[63,x]
F[80,x] = 2*F[39,x]+F[81,x]+F[97,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[90,x]
F[83,x] = F[18,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[22,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[87,x]
F[90,x] = F[54,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[57,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[94,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[48,x]+F[99,x]
F[99,x] = F[80,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{25}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{38}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{60}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right)
F_{44}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{49}\! \left(x \right) = F_{39}\! \left(x \right)+F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{46}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{26}\! \left(x \right)+F_{49}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{59}\! \left(x \right) = F_{54}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{80}\! \left(x \right)
F_{63}\! \left(x \right) = F_{39}\! \left(x \right)+F_{64}\! \left(x \right)+F_{77}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{21}\! \left(x \right)
F_{70}\! \left(x \right) = F_{31}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{35}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{34}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{63}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{81}\! \left(x \right)+F_{97}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{90}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{22}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{54}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{57}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{48}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{80}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_25(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_11(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_4(x))
Eq(F_24(x), F_18(x))
Eq(F_25(x), F_26(x) + F_38(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_14(x))
Eq(F_30(x), F_26(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_26(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)*F_4(x))
Eq(F_37(x), F_31(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_60(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_43(x) + F_7(x))
Eq(F_43(x), F_19(x))
Eq(F_44(x), F_38(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_59(x))
Eq(F_48(x), F_49(x) + F_57(x))
Eq(F_49(x), F_39(x) + F_50(x) + F_55(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_11(x) + F_18(x))
Eq(F_53(x), F_49(x) + F_54(x))
Eq(F_54(x), F_46(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_26(x) + F_49(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_48(x))
Eq(F_59(x), F_54(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_56(x) + F_62(x))
Eq(F_62(x), F_63(x) + F_80(x))
Eq(F_63(x), F_39(x) + F_64(x) + F_77(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_14(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_21(x))
Eq(F_70(x), F_31(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_35(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_74(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_34(x) + F_79(x))
Eq(F_79(x), F_63(x))
Eq(F_80(x), 2*F_39(x) + F_81(x) + F_97(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_90(x))
Eq(F_83(x), F_18(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_22(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_87(x))
Eq(F_90(x), F_54(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_57(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_94(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_48(x) + F_99(x))
Eq(F_99(x), F_80(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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": 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"obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 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