0132_0213_1203_1230_1320
Counting sequence:
1, 1, 2, 6, 19, 58, 166, 446, 1138, 2790, 6636, 15426, 35240, 79436, 177212, 392116, 861950, 1884576, 4101994, 8894386, 19221918, 41419690, 89018232, 190861606, 408329844, 871820608, 1857915176, 3952374696, 8393980378, 17798949460, 37685321926, 79677015926, 168230855770, 354745182126, 747119642532, 1571626871466, 3302294023520, 6931210228436, 14532766513844, 30440458389436, 63699282312278, 133172403486120, 278166826775362, 580526581983706, 1210537129645494, 2522238944098258, 5251201631700336, 10924640901002446, 22711339648201068, 47181963803401480, 97952840192443616, 203224202314504176, 421366857562395250, 873133464312405916, 1808192154371745502, 3742486280883321566, 7741679653970810290, 16005779960734106646, 33074414442989210844, 68310564812595331986, 141016655976444904088, 290968474834012583900, 600095497700943358892, 1237084539105085887556, 2549109065900757250094, 5250403915856538793008, 10809791030285773493146, 22246771739862653154946, 45766369436934307706958, 94115284041095976393850, 193469445012156531540456, 397564217220708854663926, 816674235742480621566180, 1677030368284414707167056, 3442605119178514663854872, 7064660182594864493407416, 14492942613315359717616010, 29722574444791840785497956, 60937416773948614204805494, 124897148219545382789593286, 255914483599279531965641098, 524220457170610300604748030, 1073526125617615150406887572, 2197827136499437007606406906, 4498412969025900770340056144, 9204761181225693315461771108, 18830228551237236415730712356, 38511540885243306159196197196, 78744592146937937483925041798, 160970890669446234600496555320, 328982565336728390344725624946, 672201441164719202290527616426, 1373184988306704365242440062310, 2804553158563183021114855600546, 5726710621025719455324824839392, 11691105729864835628119695012766, 23862532195410244794569360553180, 48695609382328677421018158318616, 99352115788031692885504163566544, 202665639703631348035071682638336, 413333323824204435239505096417058
Generating function in Maple syntax:
(3*x^9-4*x^8-15*x^7+26*x^6+3*x^5-50*x^4+60*x^3-33*x^2+9*x-1)/(x^2+x-1)/(2*x-1)^3/(x-1)^3
Generating function in latex syntax:
\frac{3 x^{9}-4 x^{8}-15 x^{7}+26 x^{6}+3 x^{5}-50 x^{4}+60 x^{3}-33 x^{2}+9 x -1}{\left(x^{2}+x -1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**9 - 4*x**8 - 15*x**7 + 26*x**6 + 3*x**5 - 50*x**4 + 60*x**3 - 33*x**2 + 9*x - 1)/((x - 1)**3*(2*x - 1)**3*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^2+x-1)*(2*x-1)^3*(x-1)^3*F(x)+3*x^9-4*x^8-15*x^7+26*x^6+3*x^5-50*x^4+60*x^3-33*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}+x -1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{3} F \! \left(x \right)+3 x^{9}-4 x^{8}-15 x^{7}+26 x^{6}+3 x^{5}-50 x^{4}+60 x^{3}-33 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/160*(576*5^(1/2)-1280)*(-1/2*5^(1/2)-1/2)^(-n)+1/160*(-576*5^(1/2)-1280)*(1/2*5^(1/2)-1/2)^(-n)+1/160*(5*n^2+15*n+670)*2^n+n^2+5*n+12)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(576 \sqrt{5}-1280\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{160}+\frac{\left(-576 \sqrt{5}-1280\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{160}+\\\frac{\left(5 n^{2}+15 n +670\right) 2^{n}}{160}+n^{2}+5 n +12 & \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) = 58
a(6) = 166
a(7) = 446
a(8) = 1138
a(9) = 2790
a(n+5) = n^2-8*a(n)+4*a(n+1)+14*a(n+2)-17*a(n+3)+7*a(n+4)-3*n-2, 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) = 58
a \! \left(6\right) = 166
a \! \left(7\right) = 446
a \! \left(8\right) = 1138
a \! \left(9\right) = 2790
a \! \left(n +5\right) = n^{2}-8 a \! \left(n \right)+4 a \! \left(n +1\right)+14 a \! \left(n +2\right)-17 a \! \left(n +3\right)+7 a \! \left(n +4\right)-3 n -2, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18371/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[12,x]*F[4,x]
F[4,x] = F[23,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[14,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[13,x]
F[23,x] = F[24,x]+F[35,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[24,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]+F[34,x]
F[29,x] = 0
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]
F[33,x] = F[28,x]
F[34,x] = F[12,x]*F[24,x]
F[35,x] = F[29,x]+F[36,x]+F[84,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[57,x]
F[38,x] = F[39,x]+F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[46,x]+F[55,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[12,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = x^2
F[52,x] = F[46,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[46,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[45,x]
F[57,x] = F[35,x]+F[58,x]
F[58,x] = 2*F[29,x]+F[59,x]+F[63,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[39,x]
F[62,x] = F[58,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[72,x]
F[65,x] = F[28,x]+F[66,x]
F[66,x] = 2*F[29,x]+F[67,x]+F[71,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[43,x]
F[70,x] = F[66,x]
F[71,x] = F[12,x]*F[65,x]
F[72,x] = F[73,x]+F[82,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[28,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[28,x]
F[79,x] = F[73,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[12,x]*F[73,x]
F[82,x] = F[83,x]
F[83,x] = F[12,x]*F[72,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[93,x]
F[86,x] = F[24,x]+F[87,x]
F[87,x] = F[29,x]+F[88,x]+F[92,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[10,x]+F[43,x]
F[91,x] = F[66,x]+F[87,x]
F[92,x] = F[12,x]*F[86,x]
F[93,x] = F[100,x]+F[94,x]
F[94,x] = F[29,x]+F[30,x]+F[95,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[27,x]+F[97,x]
F[97,x] = F[94,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[94,x]
F[100,x] = 2*F[29,x]+F[101,x]+F[67,x]
F[101,x] = F[12,x]*F[93,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)+F_{84}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{57}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = x^{2}
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{57}\! \left(x \right) = F_{35}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{39}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{72}\! \left(x \right)
F_{65}\! \left(x \right) = F_{28}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{43}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{82}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{28}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{79}\! \left(x \right) = F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{93}\! \left(x \right)
F_{86}\! \left(x \right) = F_{24}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{29}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{10}\! \left(x \right)+F_{43}\! \left(x \right)
F_{91}\! \left(x \right) = F_{66}\! \left(x \right)+F_{87}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{93}\! \left(x \right) = F_{100}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{27}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{101}\! \left(x \right)+F_{67}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_12(x)*F_4(x))
Eq(F_4(x), F_23(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_14(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_13(x))
Eq(F_23(x), F_24(x) + F_35(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_24(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x) + F_34(x))
Eq(F_29(x), 0)
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_12(x))
Eq(F_33(x), F_28(x))
Eq(F_34(x), F_12(x)*F_24(x))
Eq(F_35(x), F_29(x) + F_36(x) + F_84(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_57(x))
Eq(F_38(x), F_39(x) + F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_46(x) + F_55(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_12(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), x**2)
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_46(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_45(x))
Eq(F_57(x), F_35(x) + F_58(x))
Eq(F_58(x), 2*F_29(x) + F_59(x) + F_63(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_39(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_72(x))
Eq(F_65(x), F_28(x) + F_66(x))
Eq(F_66(x), 2*F_29(x) + F_67(x) + F_71(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_43(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_12(x)*F_65(x))
Eq(F_72(x), F_73(x) + F_82(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_28(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_28(x))
Eq(F_79(x), F_73(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_12(x)*F_73(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_12(x)*F_72(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_93(x))
Eq(F_86(x), F_24(x) + F_87(x))
Eq(F_87(x), F_29(x) + F_88(x) + F_92(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_10(x) + F_43(x))
Eq(F_91(x), F_66(x) + F_87(x))
Eq(F_92(x), F_12(x)*F_86(x))
Eq(F_93(x), F_100(x) + F_94(x))
Eq(F_94(x), F_29(x) + F_30(x) + F_95(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_27(x) + F_97(x))
Eq(F_97(x), F_94(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_12(x)*F_94(x))
Eq(F_100(x), F_101(x) + 2*F_29(x) + F_67(x))
Eq(F_101(x), F_12(x)*F_93(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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0], "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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 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": 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2, 1], "pos": [[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, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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, 1, 2], "pos": 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[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": 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