0132_0213_1023_2301
Counting sequence:
1, 1, 2, 6, 20, 61, 162, 380, 812, 1627, 3130, 5890, 10996, 20569, 38786, 73928, 142476, 277303, 544058, 1073934, 2129204, 4234293, 8437922, 16837396, 33627180, 67196051, 134321402, 268557850, 537014452, 1073909137, 2147677570, 4295190880, 8590191116, 17180162159, 34360071546, 68719854118, 137439379316, 274878385773, 549756350498, 1099512227244, 2199023923244, 4398047252683, 8796093843642, 17592186951986, 35184373089140, 70368745277641, 140737489562242, 281474978032120, 562949954865292, 1125899908417447, 2251799815399610, 4503599629233470, 9007199256762036, 18014398511670949, 36028797021331106, 72057594040483908, 144115188078611756, 288230376154679043, 576460752306614138, 1152921504610273354, 2305843009217368884, 4611686018431324673, 9223372036858988162, 18446744073714053776, 36893488147423909900, 73786976294843332831, 147573952589681874682, 295147905179358639190, 590295810358711833332, 1180591620717417870557, 2361183241434829577250, 4722366482869652605660, 9444732965739298259756, 18889465931478589146939, 37778931862957170481466, 75557863725914332691298, 151115727451828656631796, 302231454903657304013113, 604462909807314598254978, 1208925819614629186196264, 2417851639229258361514124, 4835703278458516711562263, 9671406556917033411047482, 19342813113834066809382766, 38685626227668133605393460, 77371252455336267196729621, 154742504910672534378690722, 309485009821345068741875060, 618970019642690137467478572, 1237940039285380274917892467, 2475880078570760549817898490, 4951760157141521099617059450, 9903520314283042199214500276, 19807040628566084398408470129, 39614081257132168796795466626, 79228162514264337593568484288, 158456325028528675187113511436, 316912650057057350374202523983, 633825300114114700748379473018, 1267650600228229401496732259974, 2535301200456458802993436686964
Generating function in Maple syntax:
-(4*x^7+4*x^6+5*x^5-13*x^4+18*x^3-15*x^2+6*x-1)/(2*x-1)/(x-1)^5
Generating function in latex syntax:
-\frac{4 x^{7}+4 x^{6}+5 x^{5}-13 x^{4}+18 x^{3}-15 x^{2}+6 x -1}{\left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(-4*x**7 - 4*x**6 - 5*x**5 + 13*x**4 - 18*x**3 + 15*x**2 - 6*x + 1)/((x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^5*F(x)+4*x^7+4*x^6+5*x^5-13*x^4+18*x^3-15*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+4 x^{7}+4 x^{6}+5 x^{5}-13 x^{4}+18 x^{3}-15 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,12+2^(n+1)-64/3*n+67/6*n^2-19/6*n^3+1/3*n^4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 12+2^{n +1}-\frac{64 n}{3}+\frac{67 n^{2}}{6}-\frac{19 n^{3}}{6}+\frac{n^{4}}{3} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 162
a(7) = 380
a(n+1) = -1/3*n^4+9/2*n^3-56/3*n^2+2*a(n)+71/2*n-25, n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 61
a \! \left(6\right) = 162
a \! \left(7\right) = 380
a \! \left(n +1\right) = -\frac{n^{4}}{3}+\frac{9 n^{3}}{2}-\frac{56 n^{2}}{3}+2 a \! \left(n \right)+\frac{71 n}{2}-25, \quad n \geq 8
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/21181/
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[8,x]
F[4,x] = F[21,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = 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[8,x]
F[13,x] = F[14,x]+F[6,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[8,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[15,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[25,x]+F[54,x]
F[25,x] = F[26,x]+F[34,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[33,x]
F[28,x] = 0
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[31,x]+F[8,x]
F[31,x] = F[28,x]+F[29,x]+F[32,x]
F[32,x] = F[17,x]*F[8,x]
F[33,x] = F[26,x]*F[8,x]
F[34,x] = F[35,x]+F[42,x]
F[35,x] = F[28,x]+F[36,x]+F[41,x]
F[36,x] = F[37,x]*F[8,x]
F[37,x] = F[17,x]+F[38,x]
F[38,x] = F[28,x]+F[36,x]+F[39,x]
F[39,x] = F[40,x]*F[8,x]
F[40,x] = F[17,x]+F[38,x]
F[41,x] = F[25,x]*F[8,x]
F[42,x] = 2*F[28,x]+F[43,x]+F[51,x]
F[43,x] = F[44,x]*F[8,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[32,x]
F[46,x] = 2*F[28,x]+F[43,x]+F[47,x]
F[47,x] = F[48,x]*F[8,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[8,x]
F[50,x] = F[17,x]+F[48,x]
F[51,x] = F[52,x]*F[8,x]
F[52,x] = F[48,x]+F[53,x]
F[53,x] = F[51,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]+F[6,x]
F[56,x] = F[17,x]^2
F[57,x] = F[58,x]+F[92,x]
F[58,x] = F[28,x]+F[59,x]+F[90,x]
F[59,x] = F[60,x]*F[8,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[17,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]*F[8,x]
F[64,x] = F[11,x]+F[62,x]
F[65,x] = F[66,x]+F[86,x]
F[66,x] = F[28,x]+F[67,x]+F[81,x]
F[67,x] = F[68,x]*F[8,x]
F[68,x] = F[69,x]+F[74,x]
F[69,x] = F[17,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]*F[8,x]
F[72,x] = F[73,x]+F[8,x]
F[73,x] = F[71,x]
F[74,x] = F[66,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]*F[8,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = F[79,x]
F[79,x] = F[17,x]*F[8,x]
F[80,x] = F[76,x]
F[81,x] = F[8,x]*F[82,x]
F[82,x] = F[17,x]+F[83,x]
F[83,x] = F[28,x]+F[81,x]+F[84,x]
F[84,x] = F[8,x]*F[85,x]
F[85,x] = F[17,x]+F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[8,x]*F[88,x]
F[88,x] = F[20,x]+F[89,x]
F[89,x] = F[87,x]
F[90,x] = F[8,x]*F[91,x]
F[91,x] = F[58,x]+F[6,x]
F[92,x] = F[93,x]
F[93,x] = F[8,x]*F[94,x]
F[94,x] = F[108,x]+F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[28,x]+F[97,x]+F[99,x]
F[97,x] = F[8,x]*F[98,x]
F[98,x] = F[45,x]+F[8,x]
F[99,x] = F[100,x]*F[8,x]
F[100,x] = F[17,x]+F[96,x]
F[101,x] = F[102,x]+F[38,x]
F[102,x] = 2*F[28,x]+F[103,x]+F[106,x]
F[103,x] = F[104,x]*F[8,x]
F[104,x] = F[105,x]+F[31,x]
F[105,x] = F[47,x]
F[106,x] = F[107,x]*F[8,x]
F[107,x] = F[102,x]+F[48,x]
F[108,x] = F[109,x]+F[111,x]
F[109,x] = F[110,x]
F[110,x] = F[17,x]^3
F[111,x] = F[112,x]+F[92,x]
F[112,x] = F[113,x]
F[113,x] = F[17,x]^2*F[83,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \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_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
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_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \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_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{54}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{8}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{42}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{43}\! \left(x \right)+F_{51}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{8}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{6}\! \left(x \right)
F_{56}\! \left(x \right) = F_{17} \left(x \right)^{2}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{92}\! \left(x \right)
F_{58}\! \left(x \right) = F_{28}\! \left(x \right)+F_{59}\! \left(x \right)+F_{90}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{17}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{8}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{86}\! \left(x \right)
F_{66}\! \left(x \right) = F_{28}\! \left(x \right)+F_{67}\! \left(x \right)+F_{81}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right) F_{8}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{69}\! \left(x \right) = F_{17}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{8}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{66}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right) F_{8}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{80}\! \left(x \right) = F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{17}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{28}\! \left(x \right)+F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{8}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{17}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{8}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{8}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{58}\! \left(x \right)+F_{6}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{8}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{108}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{28}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{8}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{45}\! \left(x \right)+F_{8}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{8}\! \left(x \right)
F_{100}\! \left(x \right) = F_{17}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{38}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{103}\! \left(x \right)+F_{106}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{8}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{31}\! \left(x \right)
F_{105}\! \left(x \right) = F_{47}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{8}\! \left(x \right)
F_{107}\! \left(x \right) = F_{102}\! \left(x \right)+F_{48}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{111}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{17} \left(x \right)^{3}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{92}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{83}\! \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_8(x))
Eq(F_4(x), F_21(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_8(x)*F_9(x))
Eq(F_8(x), 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_8(x))
Eq(F_13(x), F_14(x) + F_6(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_8(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_25(x) + F_54(x))
Eq(F_25(x), F_26(x) + F_34(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_33(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_31(x) + F_8(x))
Eq(F_31(x), F_28(x) + F_29(x) + F_32(x))
Eq(F_32(x), F_17(x)*F_8(x))
Eq(F_33(x), F_26(x)*F_8(x))
Eq(F_34(x), F_35(x) + F_42(x))
Eq(F_35(x), F_28(x) + F_36(x) + F_41(x))
Eq(F_36(x), F_37(x)*F_8(x))
Eq(F_37(x), F_17(x) + F_38(x))
Eq(F_38(x), F_28(x) + F_36(x) + F_39(x))
Eq(F_39(x), F_40(x)*F_8(x))
Eq(F_40(x), F_17(x) + F_38(x))
Eq(F_41(x), F_25(x)*F_8(x))
Eq(F_42(x), 2*F_28(x) + F_43(x) + F_51(x))
Eq(F_43(x), F_44(x)*F_8(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_32(x))
Eq(F_46(x), 2*F_28(x) + F_43(x) + F_47(x))
Eq(F_47(x), F_48(x)*F_8(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_8(x))
Eq(F_50(x), F_17(x) + F_48(x))
Eq(F_51(x), F_52(x)*F_8(x))
Eq(F_52(x), F_48(x) + F_53(x))
Eq(F_53(x), F_51(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x) + F_6(x))
Eq(F_56(x), F_17(x)**2)
Eq(F_57(x), F_58(x) + F_92(x))
Eq(F_58(x), F_28(x) + F_59(x) + F_90(x))
Eq(F_59(x), F_60(x)*F_8(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_17(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)*F_8(x))
Eq(F_64(x), F_11(x) + F_62(x))
Eq(F_65(x), F_66(x) + F_86(x))
Eq(F_66(x), F_28(x) + F_67(x) + F_81(x))
Eq(F_67(x), F_68(x)*F_8(x))
Eq(F_68(x), F_69(x) + F_74(x))
Eq(F_69(x), F_17(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)*F_8(x))
Eq(F_72(x), F_73(x) + F_8(x))
Eq(F_73(x), F_71(x))
Eq(F_74(x), F_66(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_77(x)*F_8(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_17(x)*F_8(x))
Eq(F_80(x), F_76(x))
Eq(F_81(x), F_8(x)*F_82(x))
Eq(F_82(x), F_17(x) + F_83(x))
Eq(F_83(x), F_28(x) + F_81(x) + F_84(x))
Eq(F_84(x), F_8(x)*F_85(x))
Eq(F_85(x), F_17(x) + F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_8(x)*F_88(x))
Eq(F_88(x), F_20(x) + F_89(x))
Eq(F_89(x), F_87(x))
Eq(F_90(x), F_8(x)*F_91(x))
Eq(F_91(x), F_58(x) + F_6(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_8(x)*F_94(x))
Eq(F_94(x), F_108(x) + F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_28(x) + F_97(x) + F_99(x))
Eq(F_97(x), F_8(x)*F_98(x))
Eq(F_98(x), F_45(x) + F_8(x))
Eq(F_99(x), F_100(x)*F_8(x))
Eq(F_100(x), F_17(x) + F_96(x))
Eq(F_101(x), F_102(x) + F_38(x))
Eq(F_102(x), F_103(x) + F_106(x) + 2*F_28(x))
Eq(F_103(x), F_104(x)*F_8(x))
Eq(F_104(x), F_105(x) + F_31(x))
Eq(F_105(x), F_47(x))
Eq(F_106(x), F_107(x)*F_8(x))
Eq(F_107(x), F_102(x) + F_48(x))
Eq(F_108(x), F_109(x) + F_111(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_17(x)**3)
Eq(F_111(x), F_112(x) + F_92(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_17(x)**2*F_83(x))
Pack JSON:
{"expansion_strats": [[{"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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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": []}, "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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]]}]]}], "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, 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