0132_0231_0321_1032_3201
Counting sequence:
1, 1, 2, 6, 19, 56, 152, 391, 968, 2330, 5490, 12722, 29090, 65794, 147458, 327938, 724482, 1591298, 3477506, 7565314, 16392194, 35389442, 76152834, 163381250, 349569026, 746061826, 1588592642, 3375366146, 7157579778, 15149826050, 32010928130, 67528294402, 142237237250, 299171315714, 628407402498, 1318286524418, 2762200842242, 5781025980418, 12086037970946, 25241522798594, 52664888983554, 109779364085762, 228629699100674, 475744937443330, 989148148137986, 2054987232313346, 4266105115770882, 8849969091969026, 18346451021070338, 38007917948960770, 78689848176672770, 162815681841070082, 336679256518033410, 695806142428741634, 1437211231084609538, 2967027729507024898, 6122080743456768002, 12625841555333185538, 26026302246574096386, 53624360763100495874, 110437270062379302914, 227341709189662638082, 467797900494228160514, 962185053188451729410, 1978269186717273554946, 4065777685996045860866, 8352916300876606341122, 17154319067045276155906, 35217140279720747728898, 72274343280794023231490, 148274928864477375889410, 304094576055101958389762, 623463056203235425517570, 1277842855474008059543554, 2618257066846038918168578, 5363132585014020198629378, 10982453551723718650101762, 22483186824942380862406658, 46014739009081822962253826, 94149820568972116625457154, 192587549904389871104950274, 393845364671328410822246402, 805220153727068944677732354, 1645876945541591707039039490, 3363382745895350192679419906, 6871534358689552229029904386, 14035628765725844718338703362, 28662422257243243103108726786, 58519263224265739830827155458, 119451542384482279494367838210, 243777473673650743821150978050, 497400439222243027641109053442, 1014685290325507475947785289730, 2069526260675334474562610921474, 4220137593923861357131114479618, 8603992758043214255617638137858, 17538515506575625044633342443522, 35744280694326070057437312843778, 72835440151394633853964872843266, 148389396629059962791608222482434, 302265343512232730961569363525634
Generating function in Maple syntax:
-(x^8-3*x^7+2*x^6+x^5-x^4+10*x^3-13*x^2+6*x-1)/(x-1)/(2*x-1)^3
Generating function in latex syntax:
-\frac{x^{8}-3 x^{7}+2 x^{6}+x^{5}-x^{4}+10 x^{3}-13 x^{2}+6 x -1}{\left(x -1\right) \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(-x**8 + 3*x**7 - 2*x**6 - x**5 + x**4 - 10*x**3 + 13*x**2 - 6*x + 1)/((x - 1)*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x-1)^3*F(x)+x^8-3*x^7+2*x^6+x^5-x^4+10*x^3-13*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x -1\right)^{3} F \! \left(x \right)+x^{8}-3 x^{7}+2 x^{6}+x^{5}-x^{4}+10 x^{3}-13 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,19,2+1/256*(5*n^2+113*n-258)*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 19 & n =4 \\ 2+\frac{\left(5 n^{2}+113 n -258\right) 2^{n}}{256} & \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) = 56
a(6) = 152
a(7) = 391
a(8) = 968
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-2, 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) = 56
a \! \left(6\right) = 152
a \! \left(7\right) = 391
a \! \left(8\right) = 968
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-2, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18658/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[17,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[11,x]+F[14,x]
F[17,x] = F[18,x]+F[46,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[28,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[26,x]+F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[11,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[1,x]+F[29,x]
F[32,x] = F[33,x]+F[34,x]+F[39,x]
F[33,x] = 0
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[11,x]+F[36,x]
F[36,x] = F[33,x]+F[34,x]+F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[29,x]+F[36,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[38,x]+F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[43,x]
F[43,x] = F[29,x]*F[4,x]
F[44,x] = F[45,x]
F[45,x] = F[36,x]*F[4,x]
F[46,x] = F[33,x]+F[47,x]+F[71,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[57,x]
F[49,x] = F[11,x]+F[50,x]
F[50,x] = F[33,x]+F[51,x]+F[56,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[16,x]+F[53,x]
F[53,x] = F[26,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[4,x]
F[56,x] = F[13,x]*F[4,x]
F[57,x] = F[36,x]+F[58,x]
F[58,x] = F[33,x]+F[59,x]+F[64,x]+F[69,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[14,x]+F[61,x]
F[61,x] = 2*F[33,x]+F[59,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[36,x]+F[61,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[63,x]+F[66,x]
F[66,x] = F[44,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[61,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[36,x]+F[61,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[18,x]+F[74,x]
F[74,x] = F[33,x]+F[47,x]+F[75,x]
F[75,x] = F[4,x]*F[73,x]
F[76,x] = F[77,x]+F[86,x]
F[77,x] = F[33,x]+F[37,x]+F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[11,x]+F[81,x]
F[81,x] = F[33,x]+F[51,x]+F[82,x]
F[82,x] = F[25,x]*F[4,x]
F[83,x] = F[36,x]+F[84,x]
F[84,x] = F[33,x]+F[59,x]+F[64,x]+F[85,x]
F[85,x] = F[4,x]*F[41,x]
F[86,x] = 2*F[33,x]+F[62,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[100,x]+F[89,x]
F[89,x] = F[14,x]+F[90,x]
F[90,x] = 2*F[33,x]+F[91,x]+F[99,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[96,x]
F[93,x] = F[14,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[93,x]
F[96,x] = F[54,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[94,x]
F[99,x] = F[4,x]*F[53,x]
F[100,x] = F[101,x]+F[61,x]
F[101,x] = 2*F[33,x]+F[102,x]+F[107,x]+F[112,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[94,x]
F[104,x] = 3*F[33,x]+F[102,x]+F[105,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[104,x]+F[61,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[106,x]+F[109,x]
F[109,x] = F[110,x]+F[67,x]
F[110,x] = F[111,x]
F[111,x] = F[104,x]*F[4,x]
F[112,x] = F[4,x]*F[66,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{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_{11}\! \left(x \right)+F_{14}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{46}\! \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_{28}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \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_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)+F_{71}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \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_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{56}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{57}\! \left(x \right) = F_{36}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right)+F_{59}\! \left(x \right)+F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{59}\! \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_{36}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{44}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{36}\! \left(x \right)+F_{61}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{86}\! \left(x \right)
F_{77}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \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_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{36}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{33}\! \left(x \right)+F_{59}\! \left(x \right)+F_{64}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{62}\! \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_{100}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{91}\! \left(x \right)+F_{99}\! \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_{14}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{96}\! \left(x \right) = F_{54}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{61}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{102}\! \left(x \right)+F_{107}\! \left(x \right)+F_{112}\! \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_{94}\! \left(x \right)
F_{104}\! \left(x \right) = 3 F_{33}\! \left(x \right)+F_{102}\! \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_{104}\! \left(x \right)+F_{61}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{67}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_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_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_11(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_46(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_28(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_11(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_1(x) + F_29(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_39(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_11(x) + F_36(x))
Eq(F_36(x), F_33(x) + F_34(x) + F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_29(x) + F_36(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_38(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_29(x)*F_4(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_36(x)*F_4(x))
Eq(F_46(x), F_33(x) + F_47(x) + F_71(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_57(x))
Eq(F_49(x), F_11(x) + F_50(x))
Eq(F_50(x), F_33(x) + F_51(x) + F_56(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_16(x) + F_53(x))
Eq(F_53(x), F_26(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_4(x))
Eq(F_56(x), F_13(x)*F_4(x))
Eq(F_57(x), F_36(x) + F_58(x))
Eq(F_58(x), F_33(x) + F_59(x) + F_64(x) + F_69(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_14(x) + F_61(x))
Eq(F_61(x), 2*F_33(x) + F_59(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_36(x) + F_61(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_63(x) + F_66(x))
Eq(F_66(x), F_44(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_61(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_36(x) + F_61(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_18(x) + F_74(x))
Eq(F_74(x), F_33(x) + F_47(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_73(x))
Eq(F_76(x), F_77(x) + F_86(x))
Eq(F_77(x), F_33(x) + F_37(x) + F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_11(x) + F_81(x))
Eq(F_81(x), F_33(x) + F_51(x) + F_82(x))
Eq(F_82(x), F_25(x)*F_4(x))
Eq(F_83(x), F_36(x) + F_84(x))
Eq(F_84(x), F_33(x) + F_59(x) + F_64(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_41(x))
Eq(F_86(x), 2*F_33(x) + F_62(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_100(x) + F_89(x))
Eq(F_89(x), F_14(x) + F_90(x))
Eq(F_90(x), 2*F_33(x) + F_91(x) + F_99(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_14(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_93(x))
Eq(F_96(x), F_54(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_94(x))
Eq(F_99(x), F_4(x)*F_53(x))
Eq(F_100(x), F_101(x) + F_61(x))
Eq(F_101(x), F_102(x) + F_107(x) + F_112(x) + 2*F_33(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_94(x))
Eq(F_104(x), F_102(x) + F_105(x) + 3*F_33(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_104(x) + F_61(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_106(x) + F_109(x))
Eq(F_109(x), F_110(x) + F_67(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_104(x)*F_4(x))
Eq(F_112(x), F_4(x)*F_66(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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 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, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 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, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 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, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [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, 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": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}], "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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [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, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [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], "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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], 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