0123_1032
Counting sequence:
1, 1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 349526, 1398102, 5592406, 22369622, 89478486, 357913942, 1431655766, 5726623062, 22906492246, 91625968982, 366503875926, 1466015503702, 5864062014806, 23456248059222, 93824992236886, 375299968947542, 1501199875790166, 6004799503160662, 24019198012642646, 96076792050570582, 384307168202282326, 1537228672809129302, 6148914691236517206, 24595658764946068822, 98382635059784275286, 393530540239137101142, 1574122160956548404566, 6296488643826193618262, 25185954575304774473046, 100743818301219097892182, 402975273204876391568726, 1611901092819505566274902, 6447604371278022265099606, 25790417485112089060398422, 103161669940448356241593686, 412646679761793424966374742, 1650586719047173699865498966, 6602346876188694799461995862, 26409387504754779197847983446, 105637550019019116791391933782, 422550200076076467165567735126, 1690200800304305868662270940502, 6760803201217223474649083762006, 27043212804868893898596335048022, 108172851219475575594385340192086, 432691404877902302377541360768342, 1730765619511609209510165443073366, 6923062478046436838040661772293462, 27692249912185747352162647089173846, 110768999648742989408650588356695382, 443075998594971957634602353426781526, 1772303994379887830538409413707126102, 7089215977519551322153637654828504406, 28356863910078205288614550619314017622, 113427455640312821154458202477256070486, 453709822561251284617832809909024281942, 1814839290245005138471331239636097127766, 7259357160980020553885324958544388511062, 29037428643920082215541299834177554044246, 116149714575680328862165199336710216176982, 464598858302721315448660797346840864707926, 1858395433210885261794643189387363458831702, 7433581732843541047178572757549453835326806, 29734326931374164188714291030197815341307222, 118937307725496656754857164120791261365228886, 475749230901986627019428656483165045460915542, 1902996923607946508077714625932660181843662166, 7611987694431786032310858503730640727374648662, 30447950777727144129243434014922562909498594646, 121791803110908576516973736059690251637994378582, 487167212443634306067894944238761006551977514326, 1948668849774537224271579776955044026207910057302, 7794675399098148897086319107820176104831640229206, 31178701596392595588345276431280704419326560916822, 124714806385570382353381105725122817677306243667286, 498859225542281529413524422900491270709224974669142, 1995436902169126117654097691601965082836899898676566, 7981747608676504470616390766407860331347599594706262, 31926990434706017882465563065631441325390398378825046, 127707961738824071529862252262525765301561593515300182, 510831846955296286119449009050103061206246374061200726, 2043327387821185144477796036200412244824985496244802902, 8173309551284740577911184144801648979299941984979211606, 32693238205138962311644736579206595917199767939916846422, 130772952820555849246578946316826383668799071759667385686, 523091811282223396986315785267305534675196287038669542742, 2092367245128893587945263141069222138700785148154678170966, 8369468980515574351781052564276888554803140592618712683862, 33477875922062297407124210257107554219212562370474850735446, 133911503688249189628496841028430216876850249481899402941782
Generating function in Maple syntax:
(x^2-4*x+1)/(4*x-1)/(x-1)
Generating function in latex syntax:
\frac{x^{2}-4 x +1}{\left(4 x -1\right) \left(x -1\right)}
Generating function in sympy syntax:
(x**2 - 4*x + 1)/((x - 1)*(4*x - 1))
Implicit equation for the generating function in Maple syntax:
(4*x-1)*(x-1)*F(x)-x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) \left(x -1\right) F \! \left(x \right)-x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,2/3+1/12*4^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{2}{3}+\frac{4^{n}}{12} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+1) = 4*a(n)-2, n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n +1\right) = 4 a \! \left(n \right)-2, \quad n \geq 3
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14595/
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[27,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[7,x]
F[14,x] = F[15,x]+F[16,x]+F[26,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]+F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[11,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[15,x]+F[16,x]+F[23,x]
F[23,x] = F[4,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[13,x]*F[4,x]
F[27,x] = F[2,x]+F[28,x]
F[28,x] = F[15,x]+F[29,x]+F[91,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[38,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[1,x]+F[4,x]
F[35,x] = F[15,x]+F[16,x]+F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[22,x]+F[7,x]
F[38,x] = F[39,x]+F[80,x]
F[39,x] = F[15,x]+F[29,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[2,x]+F[42,x]
F[42,x] = F[15,x]+F[43,x]+F[79,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[22,x]+F[4,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[15,x]+F[48,x]+F[64,x]+F[78,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[57,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[4,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[22,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = 2*F[15,x]+F[48,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[42,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[47,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[72,x]
F[66,x] = F[42,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[15,x]+F[43,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[2,x]+F[69,x]
F[72,x] = F[47,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[15,x]+F[48,x]+F[64,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[28,x]+F[75,x]
F[78,x] = F[28,x]*F[4,x]
F[79,x] = F[2,x]*F[4,x]
F[80,x] = F[15,x]+F[64,x]+F[81,x]+F[89,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[52,x]
F[85,x] = F[55,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = 2*F[15,x]+F[59,x]+F[81,x]
F[88,x] = F[62,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[28,x]+F[47,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[71,x]+F[77,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_{27}\! \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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{91}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \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_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{80}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{79}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right)+F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{64}\! \left(x \right)+F_{78}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \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_{22}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{42}\! \left(x \right)
F_{61}\! \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_{47}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{66}\! \left(x \right) = F_{42}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{47}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{64}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{28}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right)+F_{64}\! \left(x \right)+F_{81}\! \left(x \right)+F_{89}\! \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_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{52}\! \left(x \right)
F_{85}\! \left(x \right) = F_{55}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{81}\! \left(x \right)
F_{88}\! \left(x \right) = F_{62}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{28}\! \left(x \right)+F_{47}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \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_27(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_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_26(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x) + F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_11(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_23(x), F_4(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_13(x)*F_4(x))
Eq(F_27(x), F_2(x) + F_28(x))
Eq(F_28(x), F_15(x) + F_29(x) + F_91(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_38(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_1(x) + F_4(x))
Eq(F_35(x), F_15(x) + F_16(x) + F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_22(x) + F_7(x))
Eq(F_38(x), F_39(x) + F_80(x))
Eq(F_39(x), F_15(x) + F_29(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_2(x) + F_42(x))
Eq(F_42(x), F_15(x) + F_43(x) + F_79(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_22(x) + F_4(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_15(x) + F_48(x) + F_64(x) + F_78(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_57(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_4(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_22(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), 2*F_15(x) + F_48(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_42(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_47(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_72(x))
Eq(F_66(x), F_42(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_15(x) + F_43(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_2(x) + F_69(x))
Eq(F_72(x), F_47(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_15(x) + F_48(x) + F_64(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_28(x) + F_75(x))
Eq(F_78(x), F_28(x)*F_4(x))
Eq(F_79(x), F_2(x)*F_4(x))
Eq(F_80(x), F_15(x) + F_64(x) + F_81(x) + F_89(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_52(x))
Eq(F_85(x), F_55(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), 2*F_15(x) + F_59(x) + F_81(x))
Eq(F_88(x), F_62(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_28(x) + F_47(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_71(x) + F_77(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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[[1, 3], [1, 3], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 5]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 5], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}], [{"patt": [0], "pos": [[1, 5]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 5]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 5], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 4]]}], [{"patt": [0], "pos": [[1, 5]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 1], [1, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[1, 4]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 1]]}, {"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, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: regular_insertion_encoding_bottom
Tree: http://permpal.com/tree/14596/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[29,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[6,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[14,x]
F[13,x] = x
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]+F[17,x]+F[19,x]
F[16,x] = 0
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[15,x]+F[6,x]
F[19,x] = F[13,x]*F[20,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[13,x]+F[22,x]
F[22,x] = F[16,x]+F[19,x]+F[23,x]
F[23,x] = F[13,x]*F[6,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[13,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[15,x]
F[29,x] = F[16,x]+F[30,x]+F[72,x]
F[30,x] = F[13,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[2,x]+F[29,x]
F[33,x] = F[34,x]+F[53,x]
F[34,x] = F[16,x]+F[35,x]+F[37,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[2,x]+F[34,x]
F[37,x] = F[13,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[13,x]+F[40,x]
F[40,x] = F[16,x]+F[37,x]+F[41,x]
F[41,x] = F[13,x]*F[2,x]
F[42,x] = F[22,x]+F[43,x]
F[43,x] = F[16,x]+F[44,x]+F[45,x]+F[56,x]
F[44,x] = F[13,x]*F[29,x]
F[45,x] = F[13,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[40,x]+F[43,x]
F[48,x] = F[49,x]+F[51,x]
F[49,x] = F[50,x]
F[50,x] = F[13,x]*F[34,x]
F[51,x] = F[52,x]
F[52,x] = F[13,x]*F[53,x]
F[53,x] = F[16,x]+F[45,x]+F[54,x]+F[56,x]
F[54,x] = F[13,x]*F[55,x]
F[55,x] = F[29,x]+F[53,x]
F[56,x] = F[13,x]*F[57,x]
F[57,x] = F[58,x]+F[65,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[60,x]
F[60,x] = F[13,x]*F[61,x]
F[61,x] = F[13,x]
F[62,x] = 2*F[16,x]+F[56,x]+F[63,x]
F[63,x] = F[13,x]*F[64,x]
F[64,x] = F[40,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[67,x]
F[67,x] = F[13,x]*F[68,x]
F[68,x] = F[22,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[71,x]
F[71,x] = F[43,x]
F[72,x] = F[13,x]*F[73,x]
F[73,x] = F[74,x]+F[81,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[76,x]
F[76,x] = F[13,x]*F[77,x]
F[77,x] = F[1,x]+F[13,x]
F[78,x] = F[16,x]+F[72,x]+F[79,x]
F[79,x] = F[13,x]*F[80,x]
F[80,x] = F[2,x]+F[40,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[16,x]+F[19,x]+F[83,x]
F[83,x] = F[13,x]*F[84,x]
F[84,x] = F[22,x]+F[6,x]
F[85,x] = F[16,x]+F[45,x]+F[86,x]+F[88,x]
F[86,x] = F[13,x]*F[87,x]
F[87,x] = F[29,x]+F[43,x]
F[88,x] = F[13,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[60,x]
F[92,x] = 2*F[16,x]+F[63,x]+F[88,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[67,x]
F[95,x] = F[70,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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{6}\! \left(x \right)
F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)+F_{30}\! \left(x \right)+F_{72}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \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_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{53}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right)+F_{45}\! \left(x \right)+F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{29}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{13}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{13}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{56}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{40}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{22}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{43}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{81}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{78}\! \left(x \right) = F_{16}\! \left(x \right)+F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{13}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{13}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{85}\! \left(x \right) = F_{16}\! \left(x \right)+F_{45}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{29}\! \left(x \right)+F_{43}\! \left(x \right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{60}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{63}\! \left(x \right)+F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{67}\! \left(x \right)
F_{95}\! \left(x \right) = F_{70}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_29(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_14(x))
Eq(F_13(x), x)
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_19(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_13(x)*F_18(x))
Eq(F_18(x), F_15(x) + F_6(x))
Eq(F_19(x), F_13(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_13(x) + F_22(x))
Eq(F_22(x), F_16(x) + F_19(x) + F_23(x))
Eq(F_23(x), F_13(x)*F_6(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_13(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_15(x))
Eq(F_29(x), F_16(x) + F_30(x) + F_72(x))
Eq(F_30(x), F_13(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_2(x) + F_29(x))
Eq(F_33(x), F_34(x) + F_53(x))
Eq(F_34(x), F_16(x) + F_35(x) + F_37(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_2(x) + F_34(x))
Eq(F_37(x), F_13(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_13(x) + F_40(x))
Eq(F_40(x), F_16(x) + F_37(x) + F_41(x))
Eq(F_41(x), F_13(x)*F_2(x))
Eq(F_42(x), F_22(x) + F_43(x))
Eq(F_43(x), F_16(x) + F_44(x) + F_45(x) + F_56(x))
Eq(F_44(x), F_13(x)*F_29(x))
Eq(F_45(x), F_13(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_40(x) + F_43(x))
Eq(F_48(x), F_49(x) + F_51(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_13(x)*F_34(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_13(x)*F_53(x))
Eq(F_53(x), F_16(x) + F_45(x) + F_54(x) + F_56(x))
Eq(F_54(x), F_13(x)*F_55(x))
Eq(F_55(x), F_29(x) + F_53(x))
Eq(F_56(x), F_13(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_65(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_13(x)*F_61(x))
Eq(F_61(x), F_13(x))
Eq(F_62(x), 2*F_16(x) + F_56(x) + F_63(x))
Eq(F_63(x), F_13(x)*F_64(x))
Eq(F_64(x), F_40(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_13(x)*F_68(x))
Eq(F_68(x), F_22(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_71(x))
Eq(F_71(x), F_43(x))
Eq(F_72(x), F_13(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_81(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_13(x)*F_77(x))
Eq(F_77(x), F_1(x) + F_13(x))
Eq(F_78(x), F_16(x) + F_72(x) + F_79(x))
Eq(F_79(x), F_13(x)*F_80(x))
Eq(F_80(x), F_2(x) + F_40(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_16(x) + F_19(x) + F_83(x))
Eq(F_83(x), F_13(x)*F_84(x))
Eq(F_84(x), F_22(x) + F_6(x))
Eq(F_85(x), F_16(x) + F_45(x) + F_86(x) + F_88(x))
Eq(F_86(x), F_13(x)*F_87(x))
Eq(F_87(x), F_29(x) + F_43(x))
Eq(F_88(x), F_13(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_60(x))
Eq(F_92(x), 2*F_16(x) + F_63(x) + F_88(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_67(x))
Eq(F_95(x), F_70(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [1], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [], "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": "regular_insertion_encoding_bottom", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "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, 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