0123_1302_1320_3021
Counting sequence:
1, 1, 2, 6, 20, 60, 157, 384, 927, 2251, 5527, 13723, 34404, 86945, 221170, 565640, 1453014, 3746052, 9686551, 25108470, 65212497, 169643857, 441883585, 1152205273, 3006867318, 7852143095, 20516006812, 53626670534, 140221397592, 366743920026, 959406381697, 2510233709988, 6568744610259, 17190765628135, 44992814854555, 117765667226695, 308259089667384, 806919259976957, 2112309711700726, 5529623328066740, 14475769998515082, 37896071759773152, 99209146745918875, 259724633969261058, 679951011266514693, 1780100362283772205, 4660292900980154917, 12200661792424145509, 31941454981780679082, 83623219367801667251, 218927217959205832192, 573156429000606762578, 1500537987655452147564, 3928449230453936712150, 10284792815207755345765, 26925894875222170621200, 70492822004664532271079, 184552429275383164017187, 483164177591108808064351, 1264939518029991702006835, 3311653187548564672140492, 8670017630686302043823897, 22698394804593946880226490, 59425156839147561362795168, 155577055536722406588331518, 407305968842306244859126140, 1066340767979847996296058847, 2791716166770698071429385934, 7308807391067480854365387897, 19134705314678841727558585801, 50095307151016494726384440137, 131151213297572055100323778993, 343358326986315519577206785694, 898923756003032249046859949615, 2353412917410948813215146987300, 6161314948415853551543423216030, 16130531831028098942587395772224, 42230280348690234237128487724242, 110560308818363819207747869441801, 289450645303598921298275434264380, 757791625467938874579920479831227, 1983924227813450630364212936487967, 5193981051323321008632257868739555, 13598018912707212652319811101115103, 35600075659597486006998019003707168, 93202208011079120576208618460865525, 244006548262418700317081952305911102, 638817436551316777926716211961508684, 1672445760936975525287966113889082162, 4378519845340826175030063956929033176, 11463113773228592940874155344549319907, 30010821470592446903508593118430944858, 78569350630966365029028669826986367149, 205697230406987140197420835460651482405, 538522340559046554581099329682489962285, 1409869791207636551561965449704412618685, 3691087032937593216097688231391037210194, 9663391307350127448638310907839479408747, 25299086888597806073474526297769365325576, 66233869357403421138785548554553352206250, 173402521181512911036254114419661776595412
Generating function in Maple syntax:
(8*x^11-34*x^10+28*x^9+26*x^8-24*x^7-14*x^6+39*x^5-63*x^4+62*x^3-33*x^2+9*x-1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^3
Generating function in latex syntax:
\frac{8 x^{11}-34 x^{10}+28 x^{9}+26 x^{8}-24 x^{7}-14 x^{6}+39 x^{5}-63 x^{4}+62 x^{3}-33 x^{2}+9 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(8*x**11 - 34*x**10 + 28*x**9 + 26*x**8 - 24*x**7 - 14*x**6 + 39*x**5 - 63*x**4 + 62*x**3 - 33*x**2 + 9*x - 1)/((x - 1)**3*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^2*(x-1)^3*F(x)+8*x^11-34*x^10+28*x^9+26*x^8-24*x^7-14*x^6+39*x^5-63*x^4+62*x^3-33*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+8 x^{11}-34 x^{10}+28 x^{9}+26 x^{8}-24 x^{7}-14 x^{6}+39 x^{5}-63 x^{4}+62 x^{3}-33 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,-13/8,n = 1,37/8,n = 2,7,n = 3,11/2,n = 4,2,0)+1/80*(-8*5^(1/2)+40)*(3/2-1/2*5^(1/2))^(-n)+1/80*(8*5^(1/2)+40)*(3/2+1/2*5^(1/2))^(-n)+1/80*(5*n+50)*2^n+3/2*n^2-17/2*n+1
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}-\frac{13}{8} & n =0 \\ \frac{37}{8} & n =1 \\ 7 & n =2 \\ \frac{11}{2} & n =3 \\ 2 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-8 \sqrt{5}+40\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(8 \sqrt{5}+40\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(5 n +50\right) 2^{n}}{80}+\frac{3 n^{2}}{2}-\frac{17 n}{2}+1
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 60
a(6) = 157
a(7) = 384
a(8) = 927
a(9) = 2251
a(10) = 5527
a(11) = 13723
a(n+4) = -3/2*n^2-4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+23/2*n-2, n >= 12
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) = 60
a \! \left(6\right) = 157
a \! \left(7\right) = 384
a \! \left(8\right) = 927
a \! \left(9\right) = 2251
a \! \left(10\right) = 5527
a \! \left(11\right) = 13723
a \! \left(n +4\right) = -\frac{3 n^{2}}{2}-4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+\frac{23 n}{2}-2, \quad n \geq 12
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15209/
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[41,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[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[19,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[26,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[30,x]
F[38,x] = F[34,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[14,x]
F[41,x] = F[42,x]+F[77,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[17,x]*F[4,x]
F[48,x] = F[42,x]+F[49,x]
F[49,x] = F[20,x]+F[50,x]+F[75,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[46,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[23,x]*F[4,x]
F[55,x] = F[49,x]+F[56,x]
F[56,x] = 2*F[20,x]+F[57,x]+F[61,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[53,x]
F[60,x] = F[56,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[20,x]+F[64,x]+F[74,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[4,x]+F[67,x]
F[67,x] = F[54,x]
F[68,x] = F[63,x]+F[69,x]
F[69,x] = 2*F[20,x]+F[61,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[67,x]
F[73,x] = F[69,x]
F[74,x] = F[4,x]*F[42,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[42,x]+F[63,x]
F[77,x] = F[140,x]+F[20,x]+F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[89,x]
F[80,x] = F[7,x]+F[81,x]
F[81,x] = F[20,x]+F[82,x]+F[83,x]
F[82,x] = F[29,x]*F[4,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[46,x]+F[86,x]
F[86,x] = F[20,x]+F[82,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[46,x]
F[89,x] = F[77,x]+F[90,x]
F[90,x] = F[117,x]+F[139,x]+F[20,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[81,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[37,x]*F[4,x]
F[96,x] = F[90,x]+F[97,x]
F[97,x] = 2*F[20,x]+F[102,x]+F[116,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[94,x]
F[101,x] = F[97,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[109,x]
F[107,x] = F[108,x]+F[30,x]
F[108,x] = F[95,x]
F[109,x] = F[104,x]+F[110,x]
F[110,x] = 2*F[20,x]+F[102,x]+F[111,x]+F[115,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[108,x]
F[114,x] = F[110,x]
F[115,x] = 0
F[116,x] = 0
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[104,x]+F[119,x]
F[119,x] = F[120,x]+F[137,x]+F[20,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[11,x]+F[86,x]
F[123,x] = F[119,x]+F[124,x]
F[124,x] = F[117,x]+F[125,x]+F[136,x]+F[20,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[129,x]
F[127,x] = F[128,x]+F[86,x]
F[128,x] = F[95,x]
F[129,x] = F[124,x]+F[130,x]
F[130,x] = 2*F[20,x]+F[102,x]+F[131,x]+F[135,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[128,x]
F[134,x] = F[130,x]
F[135,x] = 0
F[136,x] = 0
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[42,x]
F[139,x] = 0
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]
F[142,x] = F[119,x]+F[42,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_{41}\! \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_{26}\! \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_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \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_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \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_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{77}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)+F_{75}\! \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_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{53}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right)+F_{64}\! \left(x \right)+F_{74}\! \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_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{54}\! \left(x \right)
F_{68}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{61}\! \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_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{42}\! \left(x \right)+F_{63}\! \left(x \right)
F_{77}\! \left(x \right) = F_{140}\! \left(x \right)+F_{20}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{89}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{20}\! \left(x \right)+F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{46}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{20}\! \left(x \right)+F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{46}\! \left(x \right)
F_{89}\! \left(x \right) = F_{77}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{117}\! \left(x \right)+F_{139}\! \left(x \right)+F_{20}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{93}\! \left(x \right) = F_{81}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{90}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{102}\! \left(x \right)+F_{116}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{94}\! \left(x \right)
F_{101}\! \left(x \right) = F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{30}\! \left(x \right)
F_{108}\! \left(x \right) = F_{95}\! \left(x \right)
F_{109}\! \left(x \right) = F_{104}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{102}\! \left(x \right)+F_{111}\! \left(x \right)+F_{115}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)
F_{114}\! \left(x \right) = F_{110}\! \left(x \right)
F_{115}\! \left(x \right) = 0
F_{116}\! \left(x \right) = 0
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{104}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{137}\! \left(x \right)+F_{20}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{11}\! \left(x \right)+F_{86}\! \left(x \right)
F_{123}\! \left(x \right) = F_{119}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{117}\! \left(x \right)+F_{125}\! \left(x \right)+F_{136}\! \left(x \right)+F_{20}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{129}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{86}\! \left(x \right)
F_{128}\! \left(x \right) = F_{95}\! \left(x \right)
F_{129}\! \left(x \right) = F_{124}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{102}\! \left(x \right)+F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{128}\! \left(x \right)
F_{134}\! \left(x \right) = F_{130}\! \left(x \right)
F_{135}\! \left(x \right) = 0
F_{136}\! \left(x \right) = 0
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{42}\! \left(x \right)
F_{139}\! \left(x \right) = 0
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{119}\! \left(x \right)+F_{42}\! \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_41(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_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(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_4(x))
Eq(F_33(x), F_26(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_14(x))
Eq(F_41(x), F_42(x) + F_77(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_17(x)*F_4(x))
Eq(F_48(x), F_42(x) + F_49(x))
Eq(F_49(x), F_20(x) + F_50(x) + F_75(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_23(x)*F_4(x))
Eq(F_55(x), F_49(x) + F_56(x))
Eq(F_56(x), 2*F_20(x) + F_57(x) + F_61(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_53(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_20(x) + F_64(x) + F_74(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_4(x) + F_67(x))
Eq(F_67(x), F_54(x))
Eq(F_68(x), F_63(x) + F_69(x))
Eq(F_69(x), 2*F_20(x) + F_61(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_67(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_4(x)*F_42(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_42(x) + F_63(x))
Eq(F_77(x), F_140(x) + F_20(x) + F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_89(x))
Eq(F_80(x), F_7(x) + F_81(x))
Eq(F_81(x), F_20(x) + F_82(x) + F_83(x))
Eq(F_82(x), F_29(x)*F_4(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_46(x) + F_86(x))
Eq(F_86(x), F_20(x) + F_82(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_46(x))
Eq(F_89(x), F_77(x) + F_90(x))
Eq(F_90(x), F_117(x) + F_139(x) + F_20(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_96(x))
Eq(F_93(x), F_81(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_37(x)*F_4(x))
Eq(F_96(x), F_90(x) + F_97(x))
Eq(F_97(x), F_102(x) + F_116(x) + 2*F_20(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_94(x))
Eq(F_101(x), F_97(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_109(x))
Eq(F_107(x), F_108(x) + F_30(x))
Eq(F_108(x), F_95(x))
Eq(F_109(x), F_104(x) + F_110(x))
Eq(F_110(x), F_102(x) + F_111(x) + F_115(x) + 2*F_20(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_108(x))
Eq(F_114(x), F_110(x))
Eq(F_115(x), 0)
Eq(F_116(x), 0)
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_104(x) + F_119(x))
Eq(F_119(x), F_120(x) + F_137(x) + F_20(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_11(x) + F_86(x))
Eq(F_123(x), F_119(x) + F_124(x))
Eq(F_124(x), F_117(x) + F_125(x) + F_136(x) + F_20(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_129(x))
Eq(F_127(x), F_128(x) + F_86(x))
Eq(F_128(x), F_95(x))
Eq(F_129(x), F_124(x) + F_130(x))
Eq(F_130(x), F_102(x) + F_131(x) + F_135(x) + 2*F_20(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_128(x))
Eq(F_134(x), F_130(x))
Eq(F_135(x), 0)
Eq(F_136(x), 0)
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_42(x))
Eq(F_139(x), 0)
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_119(x) + F_42(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "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, 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