0123_1302_1320_2031_3021
Counting sequence:
1, 1, 2, 6, 19, 52, 132, 326, 802, 1985, 4958, 12497, 31751, 81199, 208745, 538854, 1395481, 3622954, 9424158, 24551132, 64032532, 167153135, 436640312, 1141194791, 2983798169, 7803908077, 20415342947, 53416954716, 139785189307, 365837949640, 957527332728, 2506341395042, 6560691545686, 17174122628909, 44958455115170, 117694800265229, 308113060778171, 806618612265019, 2111691236408813, 5528352017745762, 14473158658397677, 37890711640586230, 99198151629639522, 259702093980889976, 679904831778146344, 1780005804283781627, 4660099386933664412, 12200265968238144131, 31940645741222633837, 83621565702313489945, 218923840259485302023, 573149532863677349112, 1500523913906616612271, 3928420520006312222644, 10284734268412599526620, 26925775529832045300254, 70492578810284654261386, 184551933879424153259609, 483163168784792277070118, 1264937464388561621057417, 3311649008208110472316847, 8670009127890205568323975, 22698377510771377777518257, 59425121675041670853958686, 155576984055589120963815169, 407305823574196664396403202, 1066340472831942816943228902, 2791715567251515675868954196, 7308806173582371989534976892, 19134702842815135850478664775, 50095302133502106677386395968, 131151203114969326412651282207, 343358306325962157022508970881, 898923714092029713578758673029, 2353412832408352121561533135595, 6161314776049476926801372910804, 16130531481572979210233649953251, 42230279640335261806681705664224, 110560307382764408415375724472448, 289450642394621167850573982621722, 757791619574425503958603253132542, 1983924215875308161669749836258245, 5193981027144804616339674374609642, 13598018863745716957927329525508421, 35600075560465568798598426677794019, 93202207810397434520180175459633427, 244006547856219624926566549604628917, 638817435729247220588768373161301786, 1672445759273493597498236369493376597, 4378519841975176693222936334547031630, 11463113766419922724804563832604128938, 30010821456820363966458737560178179952, 78569350603112714145107613641756064016, 205697230350660868409936032952741321939, 538522340445156070966844344391770525220, 1409869790977379704254884718573175504379, 3691087032472127761326385248028966493141, 9663391306409293018781421898916144989489, 25299086886696330173132182195524310508303, 66233869353560855256843728181266470605552, 173402521173748551109856209335494469452887
Generating function in Maple syntax:
-(3*x^7-10*x^6+9*x^5-14*x^4+24*x^3-19*x^2+7*x-1)/(2*x-1)/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
-\frac{3 x^{7}-10 x^{6}+9 x^{5}-14 x^{4}+24 x^{3}-19 x^{2}+7 x -1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-3*x**7 + 10*x**6 - 9*x**5 + 14*x**4 - 24*x**3 + 19*x**2 - 7*x + 1)/((x - 1)**3*(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)^3*F(x)+3*x^7-10*x^6+9*x^5-14*x^4+24*x^3-19*x^2+7*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)^{3} F \! \left(x \right)+3 x^{7}-10 x^{6}+9 x^{5}-14 x^{4}+24 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/20*(-2*5^(1/2)+10)*(3/2-1/2*5^(1/2))^(-n)+1/20*(2*5^(1/2)+10)*(3/2+1/2*5^(1/2))^(-n)+1/2*n^2-9/2*n+3/4*2^n+4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(-2 \sqrt{5}+10\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{\left(2 \sqrt{5}+10\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{n^{2}}{2}-\frac{9 n}{2}+\frac{3 \,2^{n}}{4}\\+4 & \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) = 52
a(6) = 132
a(7) = 326
a(n+3) = 1/2*n^2+2*a(n)-7*a(n+1)+5*a(n+2)-9/2*n+2, 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) = 19
a \! \left(5\right) = 52
a \! \left(6\right) = 132
a \! \left(7\right) = 326
a \! \left(n +3\right) = \frac{n^{2}}{2}+2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-\frac{9 n}{2}+2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18059/
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[33,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[19,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]+F[31,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[11,x]
F[30,x] = F[26,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[14,x]
F[33,x] = F[34,x]+F[69,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[17,x]*F[4,x]
F[40,x] = F[34,x]+F[41,x]
F[41,x] = F[20,x]+F[42,x]+F[67,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[38,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[23,x]*F[4,x]
F[47,x] = F[41,x]+F[48,x]
F[48,x] = 2*F[20,x]+F[49,x]+F[53,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[45,x]
F[52,x] = F[48,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[20,x]+F[56,x]+F[66,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[4,x]+F[59,x]
F[59,x] = F[46,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = 2*F[20,x]+F[53,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[59,x]
F[65,x] = F[61,x]
F[66,x] = F[34,x]*F[4,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[34,x]+F[55,x]
F[69,x] = F[20,x]+F[70,x]+F[96,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[7,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[29,x]*F[4,x]
F[75,x] = F[69,x]+F[76,x]
F[76,x] = 2*F[20,x]+F[77,x]+F[81,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[73,x]
F[80,x] = F[76,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[20,x]+F[84,x]+F[94,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[88,x]
F[86,x] = F[11,x]+F[87,x]
F[87,x] = F[74,x]
F[88,x] = F[83,x]+F[89,x]
F[89,x] = 2*F[20,x]+F[81,x]+F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[87,x]
F[93,x] = F[89,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[34,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[34,x]+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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \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_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \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_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{69}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right)+F_{42}\! \left(x \right)+F_{67}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{66}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{46}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{53}\! \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_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{34}\! \left(x \right)+F_{55}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{70}\! \left(x \right)+F_{96}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{75}\! \left(x \right) = F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{73}\! \left(x \right)
F_{80}\! \left(x \right) = F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{20}\! \left(x \right)+F_{84}\! \left(x \right)+F_{94}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{74}\! \left(x \right)
F_{88}\! \left(x \right) = F_{83}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{81}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{87}\! \left(x \right)
F_{93}\! \left(x \right) = F_{89}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{34}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{34}\! \left(x \right)+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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_33(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_31(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_26(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_14(x))
Eq(F_33(x), F_34(x) + F_69(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_17(x)*F_4(x))
Eq(F_40(x), F_34(x) + F_41(x))
Eq(F_41(x), F_20(x) + F_42(x) + F_67(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_38(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_23(x)*F_4(x))
Eq(F_47(x), F_41(x) + F_48(x))
Eq(F_48(x), 2*F_20(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_45(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_20(x) + F_56(x) + F_66(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_4(x) + F_59(x))
Eq(F_59(x), F_46(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), 2*F_20(x) + F_53(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_34(x)*F_4(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_34(x) + F_55(x))
Eq(F_69(x), F_20(x) + F_70(x) + F_96(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_7(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_29(x)*F_4(x))
Eq(F_75(x), F_69(x) + F_76(x))
Eq(F_76(x), 2*F_20(x) + F_77(x) + F_81(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_73(x))
Eq(F_80(x), F_76(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_20(x) + F_84(x) + F_94(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_88(x))
Eq(F_86(x), F_11(x) + F_87(x))
Eq(F_87(x), F_74(x))
Eq(F_88(x), F_83(x) + F_89(x))
Eq(F_89(x), 2*F_20(x) + F_81(x) + F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_87(x))
Eq(F_93(x), F_89(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_34(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_34(x) + F_83(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, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": 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