0213_0321_1320_2301
Counting sequence:
1, 1, 2, 6, 20, 63, 186, 526, 1449, 3928, 10540, 28091, 74518, 197018, 519629, 1368036, 3596792, 9446943, 24793218, 65031046, 170496561, 446851888, 1170845572, 3067257731, 8034073390, 21041253938, 55102271381, 144290726076, 377820238544, 989270652903, 2590193046810, 6781711140766, 17755745681913, 46487136517768, 121708885096924, 318645961224011, 834241883477062, 2184105459011018, 5718126033163613, 14970375719694996, 39193207284351656, 102609658450220463, 268636592700030642, 703301768917313206, 1841272012586792385, 4820520865912830688, 12620303779291233076, 33040416860239935251, 86500999577986706014, 226462687426836449378, 592887273808755175205, 1552199556211894142316, 4063712239251857383808, 10638938850393538273143, 27853107689628477963594, 72920390973891336673486, 190908078742844414168457, 499803872276239670054968, 1308503592129070124442508, 3425707012197361760164571, 8968617660635797269835126, 23480146402055594276908538, 61471822410222114016025837, 160935322557993004681439556, 421334148722521413848833880, 1103067130527100264506144063, 2887867256693837434951762146, 7560534667224528150913469926, 19793736800319979238917302609, 51820675844415874008095747728, 135668290954288571669884560100, 355184197461171698770587171491, 929884302314670240179935432078, 2434468711253726452845336080018, 6373521834988283980508306718389, 16686096800794675212984051895836, 43684768581562841107052784610352, 114368208972228047005392173217543, 299419858391789697703559477606778, 783891366316477841694157744731646, 2052254240784317418556656726845721, 5372871356489821596331298376320488, 14066359829591841735148210283145532, 36826208134099092338535276235175531, 96412264576332212739301505946499750, 252410585602151100797057016652560938, 660819492244628199487245094107657341, 1730047891160747717335429365863359476, 4529324181295643391860545203868317704, 11857924652842239336929210646513386703, 31044449777463188376293095537215428370, 81275424680011553306682093568220070166, 212781824263499926573217220373619125473, 557070048112345136471897637964985992768, 1458428320077249302960331834346036225684, 3818214912126830412644810146722517429811, 9996216416318097215445523169120305554622, 26170434336857171794634608487235978215618, 68515086594312839290344000545782787055173, 179374825446200188320168789656502698875596, 469609389744525410157705161436505941422816
Generating function in Maple syntax:
(x^6+2*x^5-4*x^4+11*x^3-13*x^2+6*x-1)/(2*x-1)/(x^2-3*x+1)/(x-1)^2
Generating function in latex syntax:
\frac{x^{6}+2 x^{5}-4 x^{4}+11 x^{3}-13 x^{2}+6 x -1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**6 + 2*x**5 - 4*x**4 + 11*x**3 - 13*x**2 + 6*x - 1)/((x - 1)**2*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2-3*x+1)*(x-1)^2*F(x)+x^6+2*x^5-4*x^4+11*x^3-13*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{6}+2 x^{5}-4 x^{4}+11 x^{3}-13 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/20*(38*5^(1/2)-70)*(3/2-1/2*5^(1/2))^(-n)+1/20*(-38*5^(1/2)-70)*(3/2+1/2*5^(1/2))^(-n)-2*n-3/4*2^n+5)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(38 \sqrt{5}-70\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{\left(-38 \sqrt{5}-70\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{20}-2 n -\frac{3 \,2^{n}}{4}+\\5 & \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) = 63
a(6) = 186
a(n+3) = 2*a(n)-7*a(n+1)+5*a(n+2)-2*n+5, n >= 7
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) = 63
a \! \left(6\right) = 186
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-2 n +5, \quad n \geq 7
Specification 1
Strategy pack name: row_placements
Tree: http://permpal.com/tree/21370/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[19,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[87,x]
F[4,x] = F[19,x]*F[5,x]
F[5,x] = F[1,x]+F[4,x]+F[41,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[20,x]*F[8,x]
F[8,x] = F[36,x]+F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]*F[19,x]
F[12,x] = F[1,x]+F[13,x]+F[25,x]
F[13,x] = F[14,x]*F[19,x]
F[14,x] = F[1,x]+F[15,x]+F[23,x]+F[24,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[19,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[12,x]*F[19,x]*F[20,x]
F[19,x] = x
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[19,x]*F[20,x]
F[23,x] = F[12,x]*F[19,x]
F[24,x] = F[14,x]*F[19,x]
F[25,x] = F[19,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[19,x]*F[27,x]
F[30,x] = F[21,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[19,x]*F[34,x]
F[34,x] = F[28,x]+F[31,x]
F[35,x] = F[19,x]*F[30,x]
F[36,x] = F[37,x]
F[37,x] = F[19,x]*F[38,x]
F[38,x] = F[36,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[19,x]*F[20,x]
F[41,x] = F[19,x]*F[42,x]
F[42,x] = F[1,x]+F[43,x]+F[6,x]+F[79,x]+F[81,x]
F[43,x] = F[19,x]*F[44,x]
F[44,x] = F[1,x]+F[45,x]+F[48,x]+F[57,x]+F[78,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[19,x]*F[47,x]
F[47,x] = F[1,x]+F[19,x]
F[48,x] = F[19,x]*F[49,x]
F[49,x] = F[1,x]+F[50,x]+F[51,x]+F[53,x]+F[55,x]+F[6,x]
F[50,x] = F[19,x]*F[49,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[19,x]*F[47,x]
F[53,x] = F[19,x]*F[54,x]
F[54,x] = F[1,x]+F[24,x]+F[50,x]+F[51,x]+F[53,x]
F[55,x] = F[56,x]
F[56,x] = F[17,x]*F[19,x]
F[57,x] = F[19,x]*F[58,x]
F[58,x] = F[59,x]+F[65,x]
F[59,x] = F[47,x]+F[60,x]
F[60,x] = F[28,x]+F[61,x]
F[61,x] = F[32,x]+F[62,x]+F[64,x]
F[62,x] = F[19,x]*F[63,x]
F[63,x] = F[19,x]+F[61,x]
F[64,x] = F[19,x]*F[28,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[21,x]+F[67,x]
F[67,x] = F[32,x]+F[68,x]+F[70,x]
F[68,x] = F[19,x]*F[69,x]
F[69,x] = F[19,x]+F[67,x]
F[70,x] = F[19,x]*F[21,x]
F[71,x] = F[31,x]+F[72,x]
F[72,x] = F[32,x]+F[73,x]+F[75,x]+F[77,x]
F[73,x] = F[19,x]*F[74,x]
F[74,x] = F[61,x]+F[72,x]
F[75,x] = F[19,x]*F[76,x]
F[76,x] = F[67,x]+F[72,x]
F[77,x] = F[19,x]*F[31,x]
F[78,x] = F[19,x]*F[26,x]
F[79,x] = F[19,x]*F[80,x]
F[80,x] = F[1,x]+F[23,x]+F[43,x]+F[6,x]+F[79,x]
F[81,x] = F[19,x]*F[82,x]
F[82,x] = F[1,x]+F[23,x]+F[81,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[19,x]*F[85,x]
F[85,x] = F[18,x]+F[86,x]
F[86,x] = 2*F[23,x]+F[1,x]+F[83,x]
F[87,x] = F[19,x]*F[88,x]
F[88,x] = F[1,x]+F[43,x]+F[81,x]+F[89,x]
F[89,x] = F[19,x]*F[90,x]
F[90,x] = F[1,x]+F[23,x]+F[43,x]+F[89,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_{19}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{87}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{36}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \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_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{25}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)+F_{6}\! \left(x \right)+F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)+F_{57}\! \left(x \right)+F_{78}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{57}\! \left(x \right) = F_{19}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{65}\! \left(x \right)
F_{59}\! \left(x \right) = F_{47}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{28}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{32}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{19}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{21}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{32}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{71}\! \left(x \right) = F_{31}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{32}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{19}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{61}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{79}\! \left(x \right) = F_{19}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{43}\! \left(x \right)+F_{6}\! \left(x \right)+F_{79}\! \left(x \right)
F_{81}\! \left(x \right) = F_{19}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{18}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{1}\! \left(x \right)+F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)+F_{81}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{19}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{43}\! \left(x \right)+F_{89}\! \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_19(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_87(x))
Eq(F_4(x), F_19(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_4(x) + F_41(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_20(x)*F_8(x))
Eq(F_8(x), F_36(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x)*F_19(x))
Eq(F_12(x), F_1(x) + F_13(x) + F_25(x))
Eq(F_13(x), F_14(x)*F_19(x))
Eq(F_14(x), F_1(x) + F_15(x) + F_23(x) + F_24(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_19(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_12(x)*F_19(x)*F_20(x))
Eq(F_19(x), x)
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_19(x)*F_20(x))
Eq(F_23(x), F_12(x)*F_19(x))
Eq(F_24(x), F_14(x)*F_19(x))
Eq(F_25(x), F_19(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_19(x)*F_27(x))
Eq(F_30(x), F_21(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_19(x)*F_34(x))
Eq(F_34(x), F_28(x) + F_31(x))
Eq(F_35(x), F_19(x)*F_30(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_19(x)*F_38(x))
Eq(F_38(x), F_36(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_19(x)*F_20(x))
Eq(F_41(x), F_19(x)*F_42(x))
Eq(F_42(x), F_1(x) + F_43(x) + F_6(x) + F_79(x) + F_81(x))
Eq(F_43(x), F_19(x)*F_44(x))
Eq(F_44(x), F_1(x) + F_45(x) + F_48(x) + F_57(x) + F_78(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_19(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_19(x))
Eq(F_48(x), F_19(x)*F_49(x))
Eq(F_49(x), F_1(x) + F_50(x) + F_51(x) + F_53(x) + F_55(x) + F_6(x))
Eq(F_50(x), F_19(x)*F_49(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_19(x)*F_47(x))
Eq(F_53(x), F_19(x)*F_54(x))
Eq(F_54(x), F_1(x) + F_24(x) + F_50(x) + F_51(x) + F_53(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_17(x)*F_19(x))
Eq(F_57(x), F_19(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_65(x))
Eq(F_59(x), F_47(x) + F_60(x))
Eq(F_60(x), F_28(x) + F_61(x))
Eq(F_61(x), F_32(x) + F_62(x) + F_64(x))
Eq(F_62(x), F_19(x)*F_63(x))
Eq(F_63(x), F_19(x) + F_61(x))
Eq(F_64(x), F_19(x)*F_28(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_21(x) + F_67(x))
Eq(F_67(x), F_32(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_19(x)*F_69(x))
Eq(F_69(x), F_19(x) + F_67(x))
Eq(F_70(x), F_19(x)*F_21(x))
Eq(F_71(x), F_31(x) + F_72(x))
Eq(F_72(x), F_32(x) + F_73(x) + F_75(x) + F_77(x))
Eq(F_73(x), F_19(x)*F_74(x))
Eq(F_74(x), F_61(x) + F_72(x))
Eq(F_75(x), F_19(x)*F_76(x))
Eq(F_76(x), F_67(x) + F_72(x))
Eq(F_77(x), F_19(x)*F_31(x))
Eq(F_78(x), F_19(x)*F_26(x))
Eq(F_79(x), F_19(x)*F_80(x))
Eq(F_80(x), F_1(x) + F_23(x) + F_43(x) + F_6(x) + F_79(x))
Eq(F_81(x), F_19(x)*F_82(x))
Eq(F_82(x), F_1(x) + F_23(x) + F_81(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_19(x)*F_85(x))
Eq(F_85(x), F_18(x) + F_86(x))
Eq(F_86(x), F_1(x) + 2*F_23(x) + F_83(x))
Eq(F_87(x), F_19(x)*F_88(x))
Eq(F_88(x), F_1(x) + F_43(x) + F_81(x) + F_89(x))
Eq(F_89(x), F_19(x)*F_90(x))
Eq(F_90(x), F_1(x) + F_23(x) + F_43(x) + F_89(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_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, 2, 1, 3], "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, 3, 2, 0], "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], "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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "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, 3, 2, 0], "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_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "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], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 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_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 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], "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, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [1, 0], [3, 0]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": 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