0132_0321_1203_1230_2130
Counting sequence:
1, 1, 2, 6, 19, 51, 126, 296, 671, 1485, 3230, 6934, 14735, 31059, 65034, 135424, 280691, 579477, 1192226, 2445638, 5003803, 10214563, 20809766, 42319624, 85926903, 174222157, 352800374, 713612774, 1441961943, 2911028323, 5871909458, 11835512512, 23839675819, 47989548789, 96549639066, 194148667510, 390227462979, 784004984723, 1574539545486, 3161088853672, 6344267104783, 12729162945677, 25533053787534, 51203553604726, 102659909871327, 205784796330291, 412424817939674, 826422640407872, 1655738487210915, 3316798410624533, 6643384468375378, 13304771226474854, 26642653826002731, 53346208961908803, 106804432896497974, 213814893448632584, 428008730835485415, 856714448237507981, 1714710854635409894, 3431779597935971014, 6867896029264024231, 13743768738745675715, 27502208879766212002, 55031402675416993920, 110112438349211045467, 220316166014958578933, 440800239260715273290, 881909308067142207510, 1764386642227330679251, 3529818047324217398963, 7061557713156748763422, 14126649833784413796904, 28259800456417613869695, 56531557727663244250701, 113085107466474207558526, 226210664547772936961238, 452495727536346131334959, 905128295139464760983571, 1810508278401326799537322, 3621479483432623632370816, 7243810421684387073921491, 14489186912940281267889045, 28981254276901179498300034, 57967806529213622888347782, 115945357554430633751011131, 231908638031296536330607331, 463850241456442993355862854, 927761115725174564209274376, 1855633752578922895439330519, 3711472624492558056091639501, 7423322522260690721914587734, 14847338958260242085794244262, 29695954222869631688497844343, 59394255939102846145601421859, 118792829591657283218683001330, 237593600696478887650361249088, 475201808112937270209803635211, 950430482172469947469163811317, 1900910378524679118109960546810, 3801911643895672361350191695542, 7603990454763993478051843457891
Generating function in Maple syntax:
-(6*x^5-2*x^4-5*x^2+4*x-1)/(2*x-1)/(x^3+x^2+x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{6 x^{5}-2 x^{4}-5 x^{2}+4 x -1}{\left(2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-6*x**5 + 2*x**4 + 5*x**2 - 4*x + 1)/((x - 1)**2*(2*x - 1)*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^3+x^2+x-1)*(x-1)^2*F(x)+6*x^5-2*x^4-5*x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+6 x^{5}-2 x^{4}-5 x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
1/528*(((276*I+92*3^(1/2))*11^(1/2)-352*I*3^(1/2)-352)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1232+((381*I-127*3^(1/2))*11^(1/2)-781*I*3^(1/2)+781)*(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*(((-276*I+92*3^(1/2))*11^(1/2)+352*I*3^(1/2)-352)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1232+((-381*I-127*3^(1/2))*11^(1/2)+781*I*3^(1/2)+781)*(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*((-184*11^(1/2)*3^(1/2)+704)*(17+3*11^(1/2)*3^(1/2))^(1/3)+254*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2)-1562*(17+3*11^(1/2)*3^(1/2))^(2/3)-1232)*(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)-n+6*2^n+2
Explicit closed form in latex syntax:
\frac{\left(\left(\left(276 \,\mathrm{I}+92 \sqrt{3}\right) \sqrt{11}-352 \,\mathrm{I} \sqrt{3}-352\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-1232+\left(\left(381 \,\mathrm{I}-127 \sqrt{3}\right) \sqrt{11}-781 \,\mathrm{I} \sqrt{3}+781\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(-276 \,\mathrm{I}+92 \sqrt{3}\right) \sqrt{11}+352 \,\mathrm{I} \sqrt{3}-352\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}-1232+\left(\left(-381 \,\mathrm{I}-127 \sqrt{3}\right) \sqrt{11}+781 \,\mathrm{I} \sqrt{3}+781\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(-184 \sqrt{11}\, \sqrt{3}+704\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+254 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}-1562 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}-1232\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}-n +6 \,2^{n}+2
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(n+4) = -2*a(n)-a(n+1)-a(n+2)+3*a(n+3)-2*n+6, 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) = 51
a \! \left(n +4\right) = -2 a \! \left(n \right)-a \! \left(n +1\right)-a \! \left(n +2\right)+3 a \! \left(n +3\right)-2 n +6, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19396/
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[12,x]*F[4,x]
F[4,x] = F[22,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[12,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[35,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,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[12,x]*F[16,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[23,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[23,x]
F[35,x] = F[18,x]+F[36,x]+F[52,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[39,x]+F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[35,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[33,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[49,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[63,x]
F[54,x] = F[23,x]+F[55,x]
F[55,x] = F[18,x]+F[56,x]+F[62,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[10,x]+F[59,x]
F[59,x] = F[44,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = F[51,x]
F[62,x] = F[12,x]*F[54,x]
F[63,x] = F[64,x]+F[74,x]
F[64,x] = F[18,x]+F[65,x]+F[73,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[12,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = x^2
F[70,x] = F[33,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[12,x]*F[33,x]
F[73,x] = F[12,x]*F[32,x]
F[74,x] = F[18,x]+F[75,x]+F[79,x]+F[81,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[43,x]
F[78,x] = F[50,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[55,x]
F[81,x] = F[12,x]*F[63,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
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_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \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_{12}\! \left(x \right) F_{25}\! \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_{12}\! \left(x \right) F_{16}\! \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_{12}\! \left(x \right) F_{32}\! \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_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)+F_{52}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{35}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{33}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{18}\! \left(x \right)+F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{44}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{51}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{64}\! \left(x \right) = F_{18}\! \left(x \right)+F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = x^{2}
F_{70}\! \left(x \right) = F_{33}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{74}\! \left(x \right) = F_{18}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{43}\! \left(x \right)
F_{78}\! \left(x \right) = F_{50}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{55}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_22(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_12(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_35(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(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_12(x)*F_16(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_23(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_23(x))
Eq(F_35(x), F_18(x) + F_36(x) + F_52(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_39(x) + F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_35(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_33(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_49(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_63(x))
Eq(F_54(x), F_23(x) + F_55(x))
Eq(F_55(x), F_18(x) + F_56(x) + F_62(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_10(x) + F_59(x))
Eq(F_59(x), F_44(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), F_51(x))
Eq(F_62(x), F_12(x)*F_54(x))
Eq(F_63(x), F_64(x) + F_74(x))
Eq(F_64(x), F_18(x) + F_65(x) + F_73(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_12(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), x**2)
Eq(F_70(x), F_33(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_12(x)*F_33(x))
Eq(F_73(x), F_12(x)*F_32(x))
Eq(F_74(x), F_18(x) + F_75(x) + F_79(x) + F_81(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_43(x))
Eq(F_78(x), F_50(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_55(x))
Eq(F_81(x), F_12(x)*F_63(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:
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