0132_0231_1023_1302_3102
Counting sequence:
1, 1, 2, 6, 19, 54, 146, 385, 998, 2554, 6473, 16283, 40713, 101281, 250859, 618982, 1522178, 3732076, 9125699, 22260020, 54178372, 131598713, 319062842, 772261494, 1866264643, 4503534543, 10853015855, 26121888767, 62798946771, 150808800250, 361790651170, 867104399746, 2076316208243, 4967595064930, 11875451021366, 28367707006449, 67715174535310, 161529380211042, 385066464235293, 917386425118563, 2184309470258453, 5197962983327837, 12362902442222907, 29389100679238366, 69829738626776514, 165840978744317864, 393685197867973411, 934157444299759520, 2215706909942318248, 5253307520293352489, 12450541710377371778, 29497474607373084318, 69859986173347489783, 165395926082054035991, 391452486809487403099, 926181801464572099067, 2190690940398492925603, 5180100247949820423986, 12245363333082518521154, 28939145947236521159230, 68372921139707743853267, 161499295667958142709198, 381371919173435085950682, 900371460925078116498529, 2125165964706012707144118, 5014933246570164958855178, 11831547460991692158713585, 27907749838197187423290027, 65813901765740186209038241, 155175287083958694096975385, 365798589695548093331556235, 862141189017612873098291606, 2031579921473368938081238018, 4786419313734096201294533540, 11274854899111974892950490371, 26554404398277868822257671884, 62530150045130100161562355980, 147221597040270855647612591577, 346564841573167262234564320458, 815699344847238967398225924998, 1919596749438749873187052303403, 4516747021022268309577143118047, 10626223033675487749689586519687, 24996025741685945217561776271351, 58789978350074376768973852870259, 138253875372670878710772789077674, 325083055066557053182067169923426, 764285535152482401131554141961530, 1796645846699369542804089679715123, 4222951028077647561413880356151674, 9924702625983873534125319892280958, 23322117238053729828330684710726353, 54798484302168766009452527251600478, 128742006052956857922116741777475826, 302429513728071892368045415166299589, 710364471005675473644870781518727027, 1668370155615057637678940823269748653, 3917947762250623916831272598724152021, 9199851547216390584188156119295664859, 21600301891453615488928921561836946190, 50710336720561403800187345680527284162
Generating function in Maple syntax:
-(x^9-4*x^8+10*x^7-15*x^6+21*x^5-28*x^4+30*x^3-20*x^2+7*x-1)/(x-1)^2/(x^3-2*x^2+3*x-1)^2
Generating function in latex syntax:
-\frac{x^{9}-4 x^{8}+10 x^{7}-15 x^{6}+21 x^{5}-28 x^{4}+30 x^{3}-20 x^{2}+7 x -1}{\left(x -1\right)^{2} \left(x^{3}-2 x^{2}+3 x -1\right)^{2}}
Generating function in sympy syntax:
(-x**9 + 4*x**8 - 10*x**7 + 15*x**6 - 21*x**5 + 28*x**4 - 30*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**2*(x**3 - 2*x**2 + 3*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(x-1)^2*(x^3-2*x^2+3*x-1)^2*F(x)+x^9-4*x^8+10*x^7-15*x^6+21*x^5-28*x^4+30*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{2} \left(x^{3}-2 x^{2}+3 x -1\right)^{2} F \! \left(x \right)+x^{9}-4 x^{8}+10 x^{7}-15 x^{6}+21 x^{5}-28 x^{4}+30 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/317400*(92*2^(1/3)*(((2*n+57/92)*23^(1/2)+I*n+17/4*I)*3^(1/2)+(6*I*n+171/92*I)*23^(1/2)+n+17/4)*(11+3*23^(1/2)*3^(1/2))^(2/3)+3910*2^(2/3)*(((1/17*n+18/391)*23^(1/2)+I*n+7/17*I)*3^(1/2)+(-3/17*I*n-54/391*I)*23^(1/2)-n-7/17)*(11+3*23^(1/2)*3^(1/2))^(1/3)+59800*n+105800)*(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)+1/317400*(-3910*2^(2/3)*(((-1/17*n-18/391)*23^(1/2)+I*n+7/17*I)*3^(1/2)+(-3/17*I*n-54/391*I)*23^(1/2)+n+7/17)*(11+3*23^(1/2)*3^(1/2))^(1/3)-92*2^(1/3)*(((-2*n-57/92)*23^(1/2)+I*n+17/4*I)*3^(1/2)+(6*I*n+171/92*I)*23^(1/2)-n-17/4)*(11+3*23^(1/2)*3^(1/2))^(2/3)+59800*n+105800)*(-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)+1/317400*(-460*2^(2/3)*(3^(1/2)*(n+18/23)*23^(1/2)-17*n-7)*(11+3*23^(1/2)*3^(1/2))^(1/3)-368*2^(1/3)*(3^(1/2)*(n+57/184)*23^(1/2)+1/2*n+17/8)*(11+3*23^(1/2)*3^(1/2))^(2/3)+59800*n+105800)*(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)-n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(92 \,2^{\frac{1}{3}} \left(\left(\left(2 n +\frac{57}{92}\right) \sqrt{23}+\mathrm{I} n +\frac{17 \,\mathrm{I}}{4}\right) \sqrt{3}+\left(6 \,\mathrm{I} n +\frac{171 \,\mathrm{I}}{92}\right) \sqrt{23}+n +\frac{17}{4}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+3910 \,2^{\frac{2}{3}} \left(\left(\left(\frac{n}{17}+\frac{18}{391}\right) \sqrt{23}+\mathrm{I} n +\frac{7 \,\mathrm{I}}{17}\right) \sqrt{3}+\left(-\frac{3 \,\mathrm{I} n}{17}-\frac{54 \,\mathrm{I}}{391}\right) \sqrt{23}-n -\frac{7}{17}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+59800 n +105800\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}}{317400}\\+\\\frac{\left(-3910 \,2^{\frac{2}{3}} \left(\left(\left(-\frac{n}{17}-\frac{18}{391}\right) \sqrt{23}+\mathrm{I} n +\frac{7 \,\mathrm{I}}{17}\right) \sqrt{3}+\left(-\frac{3 \,\mathrm{I} n}{17}-\frac{54 \,\mathrm{I}}{391}\right) \sqrt{23}+n +\frac{7}{17}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-92 \,2^{\frac{1}{3}} \left(\left(\left(-2 n -\frac{57}{92}\right) \sqrt{23}+\mathrm{I} n +\frac{17 \,\mathrm{I}}{4}\right) \sqrt{3}+\left(6 \,\mathrm{I} n +\frac{171 \,\mathrm{I}}{92}\right) \sqrt{23}-n -\frac{17}{4}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+59800 n +105800\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}}{317400}\\+\\\frac{\left(-460 \,2^{\frac{2}{3}} \left(\sqrt{3}\, \left(n +\frac{18}{23}\right) \sqrt{23}-17 n -7\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-368 \,2^{\frac{1}{3}} \left(\sqrt{3}\, \left(n +\frac{57}{184}\right) \sqrt{23}+\frac{n}{2}+\frac{17}{8}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+59800 n +105800\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}}{317400}\\-n +2 & \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) = 54
a(6) = 146
a(7) = 385
a(8) = 998
a(9) = 2554
a(n+6) = -a(n)+4*a(n+1)-10*a(n+2)+14*a(n+3)-13*a(n+4)+6*a(n+5)-n, 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) = 19
a \! \left(5\right) = 54
a \! \left(6\right) = 146
a \! \left(7\right) = 385
a \! \left(8\right) = 998
a \! \left(9\right) = 2554
a \! \left(n +6\right) = -a \! \left(n \right)+4 a \! \left(n +1\right)-10 a \! \left(n +2\right)+14 a \! \left(n +3\right)-13 a \! \left(n +4\right)+6 a \! \left(n +5\right)-n, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18787/
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[25,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[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[22,x]+F[4,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[4,x]
F[24,x] = F[19,x]
F[25,x] = F[26,x]+F[38,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[14,x]
F[30,x] = F[26,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[26,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]*F[4,x]
F[37,x] = F[31,x]
F[38,x] = F[39,x]+F[40,x]+F[75,x]
F[39,x] = 0
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[50,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[1,x]+F[43,x]
F[46,x] = F[19,x]+F[39,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[14,x]+F[49,x]
F[49,x] = F[47,x]
F[50,x] = F[51,x]+F[55,x]
F[51,x] = F[39,x]+F[40,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[26,x]+F[54,x]
F[54,x] = F[52,x]
F[55,x] = 2*F[39,x]+F[56,x]+F[72,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[71,x]
F[58,x] = F[59,x]+F[69,x]
F[59,x] = F[39,x]+F[60,x]+F[68,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[4,x]+F[63,x]
F[63,x] = F[19,x]+F[39,x]+F[64,x]
F[64,x] = F[14,x]*F[4,x]
F[65,x] = F[59,x]+F[66,x]
F[66,x] = 2*F[39,x]+F[56,x]+F[67,x]
F[67,x] = F[31,x]*F[4,x]
F[68,x] = F[26,x]*F[4,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[58,x]
F[71,x] = F[56,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[31,x]+F[74,x]
F[74,x] = F[72,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[26,x]+F[78,x]
F[78,x] = F[39,x]+F[60,x]+F[79,x]
F[79,x] = F[4,x]*F[77,x]
F[80,x] = F[31,x]+F[81,x]
F[81,x] = F[56,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_{25}\! \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_{18}\! \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_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \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_{24}\! \left(x \right)
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_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{38}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \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_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \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_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{75}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{50}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \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_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right)+F_{39}\! \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_{14}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \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_{26}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{56}\! \left(x \right)+F_{72}\! \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_{71}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{39}\! \left(x \right)+F_{60}\! \left(x \right)+F_{68}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{56}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{71}\! \left(x \right) = F_{56}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{31}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \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_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{26}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{39}\! \left(x \right)+F_{60}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{56}\! \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_25(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_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(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_24(x))
Eq(F_21(x), F_22(x) + F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_4(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_26(x) + F_38(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_14(x))
Eq(F_30(x), F_26(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_34(x) + F_37(x))
Eq(F_34(x), F_26(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)*F_4(x))
Eq(F_37(x), F_31(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_75(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_50(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_43(x))
Eq(F_46(x), F_19(x) + F_39(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_14(x) + F_49(x))
Eq(F_49(x), F_47(x))
Eq(F_50(x), F_51(x) + F_55(x))
Eq(F_51(x), F_39(x) + F_40(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_26(x) + F_54(x))
Eq(F_54(x), F_52(x))
Eq(F_55(x), 2*F_39(x) + F_56(x) + F_72(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_71(x))
Eq(F_58(x), F_59(x) + F_69(x))
Eq(F_59(x), F_39(x) + F_60(x) + F_68(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_4(x) + F_63(x))
Eq(F_63(x), F_19(x) + F_39(x) + F_64(x))
Eq(F_64(x), F_14(x)*F_4(x))
Eq(F_65(x), F_59(x) + F_66(x))
Eq(F_66(x), 2*F_39(x) + F_56(x) + F_67(x))
Eq(F_67(x), F_31(x)*F_4(x))
Eq(F_68(x), F_26(x)*F_4(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_58(x))
Eq(F_71(x), F_56(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_31(x) + F_74(x))
Eq(F_74(x), F_72(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_26(x) + F_78(x))
Eq(F_78(x), F_39(x) + F_60(x) + F_79(x))
Eq(F_79(x), F_4(x)*F_77(x))
Eq(F_80(x), F_31(x) + F_81(x))
Eq(F_81(x), F_56(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 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": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 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": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 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": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 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, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 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, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": 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{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 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, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": 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