0231_1302_2103_2301_3012
Counting sequence:
1, 1, 2, 6, 19, 50, 115, 246, 501, 986, 1897, 3594, 6739, 12550, 23267, 43010, 79357, 146246, 269313, 495710, 912163, 1678186, 3087171, 5678750, 10445461, 19212866, 35338697, 64998786, 119552259, 219891806, 404445075, 743891530, 1368230973, 2516570318, 4628695745, 8513500150, 15658769523, 28800968930, 52973242323, 97432984710, 179207200117, 329613431530, 606253620969, 1115074257466, 2050941315059, 3772269198838, 6938284776963, 12761495296722, 23472049278653, 43171829358742, 79405373940801, 146049252585166, 268626455891971, 494081082425498, 908756790910499, 1671464329236142, 3074302202580629, 5654523322736082, 10400289854561993, 19129115379888178, 35183928557196067, 64713333791656398, 119026377728751155, 218923640077614490, 402663351598033277, 740613369404410526, 1362200361080070273, 2505477082082526438, 4608290812567019987, 8475968255729629842, 15589736150379189811, 28673995218675853590, 52739699624784687605, 97003430993839745786, 178417125837300302185, 328160256455924751210, 603580813287064815251, 1110158195580289885158, 2041899265323279468579, 3755638274190634186402, 6907695735094203558013, 12705233274608117231334, 23368567283892954994561, 42981496293595275803198, 79055296852096348048867, 145405360429584578866890, 267442153575276202739715, 491902810856957129676734, 904750324861817911305109, 1664095289294051243743842, 3060748425012826284748489, 5629594039168695439820770, 10354437753475572968336963, 19044780217657094692930622, 35028812010301363101113299, 64428029981434030762406378, 118501622209392488556476349, 217958464201127882420022638, 400888116391954401738932545, 737348202802474772715459286, 1356194783395557056874442803
Generating function in Maple syntax:
(x^8+x^7-x^6-x^5+4*x^4+x^3+3*x^2-3*x+1)/(x^3+x^2+x-1)/(x-1)^3
Generating function in latex syntax:
\frac{x^{8}+x^{7}-x^{6}-x^{5}+4 x^{4}+x^{3}+3 x^{2}-3 x +1}{\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**8 + x**7 - x**6 - x**5 + 4*x**4 + x**3 + 3*x**2 - 3*x + 1)/((x - 1)**3*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^3+x^2+x-1)*(x-1)^3*F(x)+x^8+x^7-x^6-x^5+4*x^4+x^3+3*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{8}+x^{7}-x^{6}-x^{5}+4 x^{4}+x^{3}+3 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/528*(((-72*11^(1/2)+308*I)*3^(1/2)-216*I*11^(1/2)+308)*(17+3*11^(1/2)*3^(1/2))^(1/3)+880+((75*11^(1/2)+473*I)*3^(1/2)-225*I*11^(1/2)-473)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/528*(((75*11^(1/2)-473*I)*3^(1/2)+225*I*11^(1/2)-473)*(17+3*11^(1/2)*3^(1/2))^(2/3)+880+((-72*11^(1/2)-308*I)*3^(1/2)+216*I*11^(1/2)+308)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/528*((-150*11^(1/2)*3^(1/2)+946)*(17+3*11^(1/2)*3^(1/2))^(2/3)+144*3^(1/2)*11^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-616*(17+3*11^(1/2)*3^(1/2))^(1/3)+880)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)-3/2*n^2-1/2*n-8)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(\left(\left(-72 \sqrt{11}+308 \,\mathrm{I}\right) \sqrt{3}-216 \,\mathrm{I} \sqrt{11}+308\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+880+\left(\left(75 \sqrt{11}+473 \,\mathrm{I}\right) \sqrt{3}-225 \,\mathrm{I} \sqrt{11}-473\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{528}\\+\\\frac{\left(\left(\left(75 \sqrt{11}-473 \,\mathrm{I}\right) \sqrt{3}+225 \,\mathrm{I} \sqrt{11}-473\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+880+\left(\left(-72 \sqrt{11}-308 \,\mathrm{I}\right) \sqrt{3}+216 \,\mathrm{I} \sqrt{11}+308\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{528}\\+\\\frac{\left(\left(-150 \sqrt{11}\, \sqrt{3}+946\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+144 \sqrt{3}\, \sqrt{11}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-616 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+880\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{528}\\-\frac{3 n^{2}}{2}-\frac{n}{2}-8 & \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) = 50
a(6) = 115
a(7) = 246
a(8) = 501
a(n+3) = 3*n^2+a(n)+a(n+1)+a(n+2)+n+10, n >= 9
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) = 50
a \! \left(6\right) = 115
a \! \left(7\right) = 246
a \! \left(8\right) = 501
a \! \left(n +3\right) = 3 n^{2}+a \! \left(n \right)+a \! \left(n +1\right)+a \! \left(n +2\right)+n +10, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/21086/
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[28,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[21,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[15,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[7,x]
F[28,x] = F[29,x]+F[47,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[14,x]+F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[34,x]+F[35,x]+F[39,x]
F[34,x] = 0
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[15,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[15,x]+F[38,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[39,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[38,x]+F[46,x]
F[46,x] = F[44,x]
F[47,x] = F[34,x]+F[48,x]+F[90,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[60,x]
F[50,x] = F[51,x]+F[7,x]
F[51,x] = F[26,x]+F[34,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[15,x]+F[25,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[15,x]
F[59,x] = F[56,x]
F[60,x] = F[61,x]+F[81,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[15,x]+F[65,x]
F[65,x] = F[62,x]
F[66,x] = F[67,x]+F[74,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[40,x]+F[70,x]
F[70,x] = F[67,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[38,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[65,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[65,x]
F[81,x] = 2*F[34,x]+F[79,x]+F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[38,x]+F[78,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[38,x]
F[89,x] = F[86,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[96,x]
F[92,x] = F[15,x]+F[93,x]
F[93,x] = F[34,x]+F[90,x]+F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[65,x]+F[7,x]
F[96,x] = F[67,x]+F[97,x]
F[97,x] = F[75,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_{28}\! \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_{21}\! \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_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \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_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{47}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = 0
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_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{34}\! \left(x \right)+F_{48}\! \left(x \right)+F_{90}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{26}\! \left(x \right)+F_{34}\! \left(x \right)+F_{52}\! \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_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)
F_{59}\! \left(x \right) = F_{56}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{81}\! \left(x \right)
F_{61}\! \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_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \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_{40}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{67}\! \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_{38}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{65}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{65}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{38}\! \left(x \right)+F_{78}\! \left(x \right)
F_{85}\! \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_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{38}\! \left(x \right)
F_{89}\! \left(x \right) = F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{34}\! \left(x \right)+F_{90}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{65}\! \left(x \right)+F_{7}\! \left(x \right)
F_{96}\! \left(x \right) = F_{67}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{75}\! \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_28(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_21(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_4(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_7(x))
Eq(F_28(x), F_29(x) + F_47(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_14(x) + F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_39(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_15(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_15(x) + F_38(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_39(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_38(x) + F_46(x))
Eq(F_46(x), F_44(x))
Eq(F_47(x), F_34(x) + F_48(x) + F_90(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_60(x))
Eq(F_50(x), F_51(x) + F_7(x))
Eq(F_51(x), F_26(x) + F_34(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_15(x) + F_25(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_15(x))
Eq(F_59(x), F_56(x))
Eq(F_60(x), F_61(x) + F_81(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_15(x) + F_65(x))
Eq(F_65(x), F_62(x))
Eq(F_66(x), F_67(x) + F_74(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_40(x) + F_70(x))
Eq(F_70(x), F_67(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_38(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_65(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_65(x))
Eq(F_81(x), 2*F_34(x) + F_79(x) + F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_38(x) + F_78(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_38(x))
Eq(F_89(x), F_86(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_96(x))
Eq(F_92(x), F_15(x) + F_93(x))
Eq(F_93(x), F_34(x) + F_90(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_65(x) + F_7(x))
Eq(F_96(x), F_67(x) + F_97(x))
Eq(F_97(x), F_75(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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 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, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [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": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 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": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], 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