0132_0231_2301
Counting sequence:
1, 1, 2, 6, 21, 75, 262, 889, 2938, 9500, 30183, 94559, 292940, 899443, 2742038, 8312058, 25083465, 75426291, 226177810, 676773613, 2021748946, 6032325656, 17983151787, 53578703591, 159574197656, 475178305255, 1414937451182, 4213609809654, 12550074074253, 37388860800315, 111420071414878, 332142727281889, 990457333518250, 2954621294251028, 8817080028871023, 26321086055918063, 78602420839308260, 234809976172938331, 701681272141578950, 2097487140836321778, 6271733674026860241, 18758463242022609411, 56120376744430948522, 167938357833927129301, 502663882421971230466, 1504861655970800690960, 4506086498406055128627, 13495214203948784985719, 40423225263312928075568, 121100809059366252629455, 362846044315236956456798, 1087305910934537983283694, 3258593829052417198020885, 9766823076044899576332363, 29276344752956625424237558, 87764118728415401107451593, 263117805664303443514906330, 788884396257793311079702796, 2365393751376492197389396215, 7092801470221220908996182143, 21269339944654105568301728636, 63783723057177519278005165891, 191286078370732140466912190582, 573683947839589371248916337386, 1720585402496654715718947258201, 5160508473326790682379727159315, 15478189233407430910229281286722, 46425651297714868997743285803709, 139253133566436266338899670462258, 417695789781347496052352032230920, 1252917565201557922819701410944443, 3758299585289524301873461487214599, 11273690094363799273733088166763720, 33817847313592158925352596444656823, 101444950542584550821751179750229518, 304311957044379051677368377925255398, 912874879857507714875732724382784925, 2738462206916210073159224632278206811, 8214954152740610508883959057277241230, 24643711356322736119621016310445766833, 73928071000999565965625415205163114506, 221776064340685012264831871322892206596, 665306520652441285480524437043604643967, 1995861935719178829326384521645997747471, 5987432616888503513879765354860891881236, 17961890712115537964132441186566036081195, 53884590312946882313220663813204211298342, 161650897007115898163993017689337796603874, 484945057847365437046560169802741098799073, 1454814903945326566759159703634599223116835, 4364390897402217266133498581756759713406938, 13093029846056375508454244652720290120664229, 39278710435632219197688802361429347248972130, 117835125382322447646463207331495109896753408, 353502707464960167939680125372931459221550403, 1060501043704082594319381215896973980646494103, 3181484358024630896129167803706305517200141920, 9544403294979499526906485172533190979805518751, 28633077910873145075050314590923589469946631870, 85898883898430735536146062304905886332960453598, 257695724503400154915098233456302278898971800101
Generating function in Maple syntax:
-(13*x^6-61*x^5+115*x^4-104*x^3+48*x^2-11*x+1)/(x-1)/(3*x-1)/(2*x-1)/(x^2-3*x+1)^2
Generating function in latex syntax:
-\frac{13 x^{6}-61 x^{5}+115 x^{4}-104 x^{3}+48 x^{2}-11 x +1}{\left(x -1\right) \left(3 x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(-13*x**6 + 61*x**5 - 115*x**4 + 104*x**3 - 48*x**2 + 11*x - 1)/((x - 1)*(2*x - 1)*(3*x - 1)*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(x-1)*(3*x-1)*(2*x-1)*(x^2-3*x+1)^2*F(x)+13*x^6-61*x^5+115*x^4-104*x^3+48*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(3 x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+13 x^{6}-61 x^{5}+115 x^{4}-104 x^{3}+48 x^{2}-11 x +1 = 0
Explicit closed form in Maple syntax:
1/50*((5*n-17)*5^(1/2)-5*n-25)*(3/2-1/2*5^(1/2))^(-n)+1/50*((-5*n+17)*5^(1/2)-5*n-25)*(3/2+1/2*5^(1/2))^(-n)+2^n+1/2*3^n+1/2
Explicit closed form in latex syntax:
\frac{\left(\left(5 n -17\right) \sqrt{5}-5 n -25\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\frac{\left(\left(-5 n +17\right) \sqrt{5}-5 n -25\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{50}+2^{n}+\frac{3^{n}}{2}+\frac{1}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(6) = 262
a(n+6) = -6*a(n)+41*a(n+1)-97*a(n+2)+97*a(n+3)-47*a(n+4)+11*a(n+5)+1, 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) = 21
a \! \left(5\right) = 75
a \! \left(6\right) = 262
a \! \left(n +6\right) = -6 a \! \left(n \right)+41 a \! \left(n +1\right)-97 a \! \left(n +2\right)+97 a \! \left(n +3\right)-47 a \! \left(n +4\right)+11 a \! \left(n +5\right)+1, \quad n \geq 7
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/271/
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[22,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[17,x]
F[21,x] = F[13,x]*F[4,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[45,x]
F[26,x] = F[27,x]+F[44,x]
F[27,x] = F[18,x]+F[28,x]+F[38,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[1,x]+F[28,x]+F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[1,x]+F[32,x]+F[33,x]+F[37,x]
F[32,x] = F[31,x]*F[4,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[1,x]+F[30,x]+F[35,x]+F[36,x]
F[35,x] = F[34,x]*F[4,x]
F[36,x] = F[34,x]*F[4,x]
F[37,x] = F[31,x]*F[4,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[18,x]+F[32,x]+F[40,x]+F[43,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[18,x]+F[35,x]+F[38,x]+F[42,x]
F[42,x] = F[4,x]*F[41,x]
F[43,x] = F[39,x]*F[4,x]
F[44,x] = F[14,x]*F[7,x]
F[45,x] = F[46,x]+F[87,x]
F[46,x] = F[47,x]+F[53,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[14,x]*F[6,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[7,x]
F[52,x] = F[23,x]+F[49,x]
F[53,x] = F[54,x]+F[64,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[16,x]*F[2,x]
F[58,x] = F[16,x]*F[59,x]
F[59,x] = F[14,x]+F[60,x]
F[60,x] = F[18,x]+F[61,x]+F[63,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[14,x]+F[60,x]
F[63,x] = F[4,x]*F[59,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[60,x]+F[64,x]
F[69,x] = F[70,x]
F[70,x] = F[14,x]^2*F[7,x]
F[71,x] = F[72,x]+F[85,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[60,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[14,x]^2*F[7,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[60,x]+F[77,x]
F[80,x] = F[81,x]
F[81,x] = F[14,x]^2*F[82,x]
F[82,x] = F[18,x]+F[38,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[18,x]+F[30,x]+F[83,x]
F[85,x] = F[86,x]
F[86,x] = F[16,x]*F[64,x]
F[87,x] = F[23,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[87,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_{22}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{45}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{32}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)+F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{87}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = F_{23}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{64}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{14}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{85}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{60}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{83}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{64}\! \left(x \right)
F_{87}\! \left(x \right) = F_{23}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \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_22(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_17(x))
Eq(F_21(x), F_13(x)*F_4(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_45(x))
Eq(F_26(x), F_27(x) + F_44(x))
Eq(F_27(x), F_18(x) + F_28(x) + F_38(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_1(x) + F_28(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_1(x) + F_32(x) + F_33(x) + F_37(x))
Eq(F_32(x), F_31(x)*F_4(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_1(x) + F_30(x) + F_35(x) + F_36(x))
Eq(F_35(x), F_34(x)*F_4(x))
Eq(F_36(x), F_34(x)*F_4(x))
Eq(F_37(x), F_31(x)*F_4(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_18(x) + F_32(x) + F_40(x) + F_43(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_18(x) + F_35(x) + F_38(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_41(x))
Eq(F_43(x), F_39(x)*F_4(x))
Eq(F_44(x), F_14(x)*F_7(x))
Eq(F_45(x), F_46(x) + F_87(x))
Eq(F_46(x), F_47(x) + F_53(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_14(x)*F_6(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_7(x))
Eq(F_52(x), F_23(x) + F_49(x))
Eq(F_53(x), F_54(x) + F_64(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_16(x)*F_2(x))
Eq(F_58(x), F_16(x)*F_59(x))
Eq(F_59(x), F_14(x) + F_60(x))
Eq(F_60(x), F_18(x) + F_61(x) + F_63(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_14(x) + F_60(x))
Eq(F_63(x), F_4(x)*F_59(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_60(x) + F_64(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_14(x)**2*F_7(x))
Eq(F_71(x), F_72(x) + F_85(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_60(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_14(x)**2*F_7(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_60(x) + F_77(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_14(x)**2*F_82(x))
Eq(F_82(x), F_18(x) + F_38(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_18(x) + F_30(x) + F_83(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_16(x)*F_64(x))
Eq(F_87(x), F_23(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_87(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, 3, 1], "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, 3, 1], "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, 3, 1], "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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], 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