0231_0321_2130_3102
Counting sequence:
1, 1, 2, 6, 20, 61, 169, 440, 1103, 2702, 6525, 15613, 37129, 87912, 207482, 488460, 1147660, 2692106, 6306471, 14756756, 34497074, 80579299, 188090556, 438790041, 1023127878, 2384612996, 5555810778, 12940208935, 30131367355, 70144992847, 163263448141, 379933716433, 884023226132, 2056673653747, 4784324145071, 11128480192650, 25883129618597, 60196079969056, 139989115568987, 325535625799511, 756979345053047, 1760165136775234, 4092690821310600, 9515958486016526, 22125132853367050, 51441120211704676, 119598949019047469, 278059530696401150, 646461396681414248, 1502943242507688957, 3494124794531040490, 8123265954607958563, 18885124835967083964, 43904234030611574582, 102068251649298911712, 237286478272221463225, 551637298647839725985, 1282427457246698332041, 2981334785113283343491, 6930867804287585763011, 16112523429469474273714, 37457493724119705316149, 87078950636054094517341, 202435684926085029898236, 470609241303651971383883, 1094040492841610679685986, 2543349057137154587813353, 5912596179618977298699745, 13745172422598399246651925, 31953756976042729423354252, 74283688283247030461425606, 172689055361647358556151808, 401454210577277397712819192, 933269537457357813575298542, 2169591902910312618031844451, 5043696157055792853008623640, 11725184828128697593239214222, 27257775323833992605135704391, 63366694973598721308744234632, 147309804103853567962814358941, 342453967693390637183318008162, 796109329856450263547524930584, 1850730538307196617467663909910, 4302428282943627028949081424571, 10001935822156032248375084476855, 23251686879054227570526040672691, 54053628156126621775439606848169, 125659468293092195496966968390885, 292122878967407076637198021575168, 679103415514822472946400313640487, 1578724130988063485568373023855355, 3670088789072588636462718781243038, 8531922217097733509224215240420449, 19834314596818630936368390444149652, 46109190930698102819225078155884967, 107190871386284956878373905865839515, 249188558035737649501462425822020835, 579293144548261844703709492074509126, 1346693233525436606260267426813802036, 3130682058647206607422225514851357666, 7277953031702374111544610768474871254
Generating function in Maple syntax:
-(x^9-2*x^8+x^7+5*x^6-16*x^5+25*x^4-29*x^3+20*x^2-7*x+1)/(2*x-1)/(x^3-2*x^2+3*x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{9}-2 x^{8}+x^{7}+5 x^{6}-16 x^{5}+25 x^{4}-29 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**9 + 2*x**8 - x**7 - 5*x**6 + 16*x**5 - 25*x**4 + 29*x**3 - 20*x**2 + 7*x - 1)/((x - 1)**3*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^3-2*x^2+3*x-1)*(x-1)^3*F(x)+x^9-2*x^8+x^7+5*x^6-16*x^5+25*x^4-29*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{9}-2 x^{8}+x^{7}+5 x^{6}-16 x^{5}+25 x^{4}-29 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/13800*(-368*((I-7/184*23^(1/2))*3^(1/2)-21/184*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+9200-115*2^(2/3)*((I+19/23*23^(1/2))*3^(1/2)-57/23*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(11/600*2^(1/3)*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(115*2^(2/3)*((I-19/23*23^(1/2))*3^(1/2)-57/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+368*2^(1/3)*((I+7/184*23^(1/2))*3^(1/2)-21/184*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*2^(1/3)*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*((190*3^(1/2)*2^(2/3)*23^(1/2)-230*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+(-28*23^(1/2)*3^(1/2)*2^(1/3)+736*2^(1/3))*(11+3*23^(1/2)*3^(1/2))^(2/3))*(1/300*2^(1/3)*(3*23^(1/2)*3^(1/2)-11)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/6*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)-1/2*n^2-3/2*n-9/8*2^n+3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(-368 \left(\left(\mathrm{I}-\frac{7 \sqrt{23}}{184}\right) \sqrt{3}-\frac{21 \,\mathrm{I} \sqrt{23}}{184}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+9200-115 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{19 \sqrt{23}}{23}\right) \sqrt{3}-\frac{57 \,\mathrm{I} \sqrt{23}}{23}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}-\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(115 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{19 \sqrt{23}}{23}\right) \sqrt{3}-\frac{57 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+368 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{7 \sqrt{23}}{184}\right) \sqrt{3}-\frac{21 \,\mathrm{I} \sqrt{23}}{184}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(\left(190 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}-230 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+\left(-28 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+736 \,2^{\frac{1}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(3 \sqrt{23}\, \sqrt{3}-11\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{300}-\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{13800}\\-\frac{n^{2}}{2}-\frac{3 n}{2}-\frac{9 \,2^{n}}{8}+3 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 169
a(7) = 440
a(8) = 1103
a(9) = 2702
a(n+4) = -1/2*n^2-2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)-3/2*n+4, n >= 10
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) = 61
a \! \left(6\right) = 169
a \! \left(7\right) = 440
a \! \left(8\right) = 1103
a \! \left(9\right) = 2702
a \! \left(n +4\right) = -\frac{n^{2}}{2}-2 a \! \left(n \right)+5 a \! \left(n +1\right)-8 a \! \left(n +2\right)+5 a \! \left(n +3\right)-\frac{3 n}{2}+4, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15854/
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[17,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[6,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[14,x]+F[7,x]
F[17,x] = F[18,x]+F[34,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[26,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[11,x]
F[26,x] = F[18,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[26,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[18,x]+F[31,x]
F[34,x] = F[35,x]+F[36,x]+F[73,x]
F[35,x] = 0
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[52,x]
F[38,x] = F[39,x]+F[7,x]
F[39,x] = F[35,x]+F[40,x]+F[43,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[38,x]+F[42,x]
F[42,x] = F[14,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[11,x]+F[46,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[14,x]+F[49,x]
F[52,x] = F[53,x]+F[69,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[57,x]+F[7,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[56,x]+F[60,x]
F[60,x] = F[14,x]
F[61,x] = F[53,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[61,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[53,x]+F[66,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[52,x]+F[72,x]
F[72,x] = F[66,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[17,x]+F[75,x]
F[75,x] = F[76,x]+F[85,x]
F[76,x] = F[32,x]+F[35,x]+F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[11,x]+F[80,x]
F[80,x] = F[35,x]+F[81,x]+F[83,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[79,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[11,x]
F[85,x] = 2*F[35,x]+F[67,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[14,x]+F[89,x]
F[89,x] = 2*F[35,x]+F[90,x]+F[92,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[88,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[14,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_{17}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \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_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \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_{26}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \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_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{73}\! \left(x \right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{52}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{7}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{69}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{53}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{52}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{66}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{85}\! \left(x \right)
F_{76}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{35}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{79}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{67}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \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_17(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_6(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_14(x) + F_7(x))
Eq(F_17(x), F_18(x) + F_34(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_26(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_11(x))
Eq(F_26(x), F_18(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_26(x) + F_30(x))
Eq(F_30(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_18(x) + F_31(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_73(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_52(x))
Eq(F_38(x), F_39(x) + F_7(x))
Eq(F_39(x), F_35(x) + F_40(x) + F_43(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_38(x) + F_42(x))
Eq(F_42(x), F_14(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_11(x) + F_46(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_14(x) + F_49(x))
Eq(F_52(x), F_53(x) + F_69(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_57(x) + F_7(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_56(x) + F_60(x))
Eq(F_60(x), F_14(x))
Eq(F_61(x), F_53(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_61(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_53(x) + F_66(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_52(x) + F_72(x))
Eq(F_72(x), F_66(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_17(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_85(x))
Eq(F_76(x), F_32(x) + F_35(x) + F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_11(x) + F_80(x))
Eq(F_80(x), F_35(x) + F_81(x) + F_83(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_79(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_11(x))
Eq(F_85(x), 2*F_35(x) + F_67(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_14(x) + F_89(x))
Eq(F_89(x), 2*F_35(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_88(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_14(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, 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": [2, 1, 3, 0], "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, 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": [2, 1, 3, 0], "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, 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": [2, 1, 3, 0], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [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": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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]]}], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [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, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [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": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [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]]}], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [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": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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]]}], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [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": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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]]}], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[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, 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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [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": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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