0132_0231_0321_3012_3102
Counting sequence:
1, 1, 2, 6, 19, 53, 142, 380, 1013, 2695, 7168, 19062, 50687, 134777, 358370, 952896, 2533721, 6737083, 17913684, 47631898, 126651651, 336762573, 895440598, 2380947076, 6330859901, 16833548079, 44759850216, 119014968318, 316456883015, 841448434785, 2237383689226, 5949129579272, 15818539717345, 42060976392419, 111838751660732, 297375559148578, 790711822742731, 2102476707955509, 5590416356950910, 14864733067342796, 39524835907547525, 105095237596339671, 279444777234912464, 743034463881259654, 1975704180190111119, 5253332378731306825, 13968437865415244082, 37141616469942017232, 98758335562761892201, 262595163326296289803, 698231895155238506276, 1856575624762297086762, 4936573471332425259411, 13126186357737624618141, 34902097436332268669222, 92803528173067012475412, 246761526497941542856333, 656130776041614635526527, 1744630134927304838860216, 4638914098892107398959630, 12334719884794748907832535, 32797614138336214892345137, 87207776359251393490442074, 231882606626428499688894360, 616568217888780822652921073, 1639434595122492931975620659, 4359202621386623685981951116, 11590976273673301949245365042, 30820024358978213448423922523, 81949430234402976218057112325, 217900837375130769783028877262, 579391153702620942680962711900, 1540582005249178607581068525717, 4096356838951239697409157517863, 10892077990556899887761308985248, 28961676830563396688093912539798, 77008145329586172658767449100575, 204762123470849541781151428711449, 544455745932412049597258131603074, 1447689905994845986293202590118752, 3849359804863803105745966169263481, 10235321007587276296979651191851867, 27215381632028047672291673733204724, 72364803881370977853054930996788282, 192415631409944555972360838110485027, 511626829965316185142359954684167789, 1360398899103318881963190609472397174, 3617255890991843061013462849849932196, 9618164341017637374274836218540597149, 25574382371233755573489516505875920847, 68001440865468834643280794929992303240, 180813592784206699608600778802941721630, 480777391176349745007461385547627588199, 1278371256867843858910085139758181504513, 3399147090480450862044833222669874040490, 9038220220181445073014674356193184761896, 24032330044579028725894352214572606573313, 63901174490300404248893045230678145989507, 169911119465542727369709791388315268076124, 451788073510543916440101332436453895288386, 1201289615467231368747698546722579350631915
Generating function in Maple syntax:
(2*x^5+4*x^4-2*x+1)/(x-1)/(2*x^3+x^2+2*x-1)
Generating function in latex syntax:
\frac{2 x^{5}+4 x^{4}-2 x +1}{\left(x -1\right) \left(2 x^{3}+x^{2}+2 x -1\right)}
Generating function in sympy syntax:
(2*x**5 + 4*x**4 - 2*x + 1)/((x - 1)*(2*x**3 + x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(2*x^3+x^2+2*x-1)*F(x)+2*x^5+4*x^4-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(2 x^{3}+x^{2}+2 x -1\right) F \! \left(x \right)+2 x^{5}+4 x^{4}-2 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/342672*(((7139*I-1089*59^(1/2))*3^(1/2)-3267*I*59^(1/2)+7139)*(71+6*59^(1/2)*3^(1/2))^(1/3)-28556+((5369*I+285*59^(1/2))*3^(1/2)-855*I*59^(1/2)-5369)*(71+6*59^(1/2)*3^(1/2))^(2/3))*(1/1452*((71*I+6*59^(1/2))*3^(1/2)-18*I*59^(1/2)-71)*(71+6*59^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/12*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6)^(-n)+1/342672*(((-5369*I+285*59^(1/2))*3^(1/2)+855*I*59^(1/2)-5369)*(71+6*59^(1/2)*3^(1/2))^(2/3)-28556+((-7139*I-1089*59^(1/2))*3^(1/2)+3267*I*59^(1/2)+7139)*(71+6*59^(1/2)*3^(1/2))^(1/3))*(1/1452*((-71*I+6*59^(1/2))*3^(1/2)+18*I*59^(1/2)-71)*(71+6*59^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/12*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6)^(-n)-5/4+1/342672*((-570*59^(1/2)*3^(1/2)+10738)*(71+6*59^(1/2)*3^(1/2))^(2/3)+2178*(71+6*59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/2)-14278*(71+6*59^(1/2)*3^(1/2))^(1/3)-28556)*(1/6*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6+71/726*(71+6*59^(1/2)*3^(1/2))^(2/3)-1/121*(71+6*59^(1/2)*3^(1/2))^(2/3)*59^(1/2)*3^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(\left(\left(7139 \,\mathrm{I}-1089 \sqrt{59}\right) \sqrt{3}-3267 \,\mathrm{I} \sqrt{59}+7139\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-28556+\left(\left(5369 \,\mathrm{I}+285 \sqrt{59}\right) \sqrt{3}-855 \,\mathrm{I} \sqrt{59}-5369\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(71 \,\mathrm{I}+6 \sqrt{59}\right) \sqrt{3}-18 \,\mathrm{I} \sqrt{59}-71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{1452}-\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{1}{6}\right)^{-n}}{342672}\\+\\\frac{\left(\left(\left(-5369 \,\mathrm{I}+285 \sqrt{59}\right) \sqrt{3}+855 \,\mathrm{I} \sqrt{59}-5369\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}-28556+\left(\left(-7139 \,\mathrm{I}-1089 \sqrt{59}\right) \sqrt{3}+3267 \,\mathrm{I} \sqrt{59}+7139\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-71 \,\mathrm{I}+6 \sqrt{59}\right) \sqrt{3}+18 \,\mathrm{I} \sqrt{59}-71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{1452}+\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{1}{6}\right)^{-n}}{342672}\\-\frac{5}{4}+\\\frac{\left(\left(-570 \sqrt{59}\, \sqrt{3}+10738\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}+2178 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, \sqrt{3}-14278 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-28556\right) \left(\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{6}+\frac{71 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{726}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{59}\, \sqrt{3}}{121}\right)^{-n}}{342672} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(n+3) = 2*a(n)+a(n+1)+2*a(n+2)+5, n >= 6
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) = 19
a \! \left(5\right) = 53
a \! \left(n +3\right) = 2 a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)+5, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18740/
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[22,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[4,x]
F[22,x] = F[23,x]+F[35,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[16,x]*F[4,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[23,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[23,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]+F[75,x]
F[36,x] = 0
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[50,x]
F[39,x] = F[40,x]+F[7,x]
F[40,x] = F[36,x]+F[41,x]+F[42,x]
F[41,x] = F[19,x]*F[4,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[20,x]+F[4,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]
F[47,x] = x^2
F[48,x] = F[49,x]
F[49,x] = F[20,x]*F[4,x]
F[50,x] = F[35,x]+F[51,x]
F[51,x] = 2*F[36,x]+F[52,x]+F[68,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[64,x]
F[54,x] = F[36,x]+F[55,x]+F[66,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[11,x]+F[58,x]
F[58,x] = F[36,x]+F[41,x]+F[59,x]
F[59,x] = F[4,x]*F[44,x]
F[60,x] = F[54,x]+F[61,x]
F[61,x] = 2*F[36,x]+F[52,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[33,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[54,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[23,x]+F[54,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[63,x]+F[70,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[72,x]
F[72,x] = F[33,x]*F[4,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[64,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[67,x]+F[77,x]
F[77,x] = F[78,x]+F[88,x]
F[78,x] = F[36,x]+F[79,x]+F[87,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[4,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = x^2
F[84,x] = F[33,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[33,x]*F[4,x]
F[87,x] = F[32,x]*F[4,x]
F[88,x] = 2*F[36,x]+F[89,x]+F[97,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]+F[94,x]
F[91,x] = F[20,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[20,x]*F[4,x]
F[94,x] = F[64,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[64,x]
F[97,x] = F[4,x]*F[53,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_{22}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{75}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{50}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = x^{2}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{35}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{52}\! \left(x \right)+F_{68}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{64}\! \left(x \right)
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)+F_{55}\! \left(x \right)+F_{66}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{60}\! \left(x \right) = F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{52}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{33}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{67}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{88}\! \left(x \right)
F_{78}\! \left(x \right) = F_{36}\! \left(x \right)+F_{79}\! \left(x \right)+F_{87}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \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_{83}\! \left(x \right) = x^{2}
F_{84}\! \left(x \right) = F_{33}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{87}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{89}\! \left(x \right)+F_{97}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{91}\! \left(x \right) = F_{20}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{94}\! \left(x \right) = F_{64}\! \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_{64}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \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_22(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_35(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_16(x)*F_4(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_23(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_23(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_75(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_50(x))
Eq(F_39(x), F_40(x) + F_7(x))
Eq(F_40(x), F_36(x) + F_41(x) + F_42(x))
Eq(F_41(x), F_19(x)*F_4(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_20(x) + F_4(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), x**2)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_20(x)*F_4(x))
Eq(F_50(x), F_35(x) + F_51(x))
Eq(F_51(x), 2*F_36(x) + F_52(x) + F_68(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_64(x))
Eq(F_54(x), F_36(x) + F_55(x) + F_66(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_11(x) + F_58(x))
Eq(F_58(x), F_36(x) + F_41(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_44(x))
Eq(F_60(x), F_54(x) + F_61(x))
Eq(F_61(x), 2*F_36(x) + F_52(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_33(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_54(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_23(x) + F_54(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_63(x) + F_70(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_33(x)*F_4(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_64(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_67(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_88(x))
Eq(F_78(x), F_36(x) + F_79(x) + F_87(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_4(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), x**2)
Eq(F_84(x), F_33(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_33(x)*F_4(x))
Eq(F_87(x), F_32(x)*F_4(x))
Eq(F_88(x), 2*F_36(x) + F_89(x) + F_97(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_94(x))
Eq(F_91(x), F_20(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_20(x)*F_4(x))
Eq(F_94(x), F_64(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_64(x))
Eq(F_97(x), F_4(x)*F_53(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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 1, 2], "pos": [[0, 0], [0, 0], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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]]}], "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, 1, 2], "pos": [[1, 0], [1, 0], [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": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"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, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"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]]}], "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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 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, 2], "pos": [[0, 0], [0, 0], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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]]}], "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, 2], "pos": [[0, 0], [0, 0], [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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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]]}], "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], "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, 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