0132_2130
Counting sequence:
1, 1, 2, 6, 22, 86, 337, 1299, 4910, 18228, 66640, 240550, 859295, 3043525, 10705182, 37441618, 130351650, 452119862, 1563402141, 5392828631, 18564966510, 63807048144, 219015409556, 750968486726, 2572756726459, 8808011192329, 30138217809470, 103077794599470, 352418479793638, 1204561546553558, 4116241406917369, 14063521710289371, 48042400660943246, 164098817957084652, 560462502814040728, 1914062823740726758, 6536433380113471703, 22320591420369886669, 76217532865157026398, 260250565358216027530, 888625316943173648682, 3034156300494428525174, 10359793881559564959957, 35371988118944179741535, 120771382286064443357358, 412349640933539016294792, 1407877465866269858688284, 4806868593771338206588550, 16411874693235775212844915, 56034176862989778691725841, 191314068388646884866139262, 653190887201205444260682342, 2230143339124013418031002094, 7614212750235349732846635542, 25996620827394699725414961457, 88758208582963603776968935779, 303039994850237194056808728014, 1034644634621710350152147064996, 3532501407340037437386602707744, 12060723977450352568382132940070, 41177913387179662350260810076815, 140590259634433381030642639587541, 480005355639873294243619073637534, 1638841286237867517602504397409474, 5595355452665314348668064751948850, 19103741948945794562519572015599542, 65224264099891630758172261125558285, 222689591670960731004437374520008679, 760309889441512594173967337391282414, 2595860509852576951687234848960300864, 8862822620372264293379554976210552996, 30259570417716296705950995700371233222, 103312638969033455717453172132139273771, 352731421782563128559351853680797754905, 1204300427091065604066521640368527137470, 4111738912309479668062296101692389701790, 14038354921142427100829632982540826493942, 47929942194508226397893527405354519929686, 163643059823303060422489418221770490601833, 558712357258403086763288638896111433949931, 1907563315630403138412047558054508758610446, 6512828564559680153649293618604340955074908, 22236187670867479722878706665682871994659240, 75919093670690513561399628976468029056791654, 259203999649367451155741751645215496287473223, 884977812073173929423660441171851843823660509, 3021503251158877971487201986881028331136171742, 10316057386224432475725550304974845764044808698, 35221223057771666489712751210772218100884790586, 120252777498872421035945702043570119492406576374, 410568663986492147043637934717620429507310201157, 1401769101230332587794425993205922394809341120111, 4785939077695211380210424968208156689673000931630, 16340218110297215180610544808669515100180578286328, 55788994291031235674118858640307959250917054026284, 190475540957378998515933070381929682639308318850310, 650324175284099008655520278781488423363651837015779, 2220345619318597356680130760880030902075630075534369, 7580734126962705097980669168472699523368740265961726, 25882245269892179729459937157295027339202324481707222, 88367512827438092881579957820122610061704382313430014
Generating function in Maple syntax:
-(2*x-1)*(2*x^5-12*x^4+24*x^3-22*x^2+8*x-1)/(x-1)/(2*x^2-4*x+1)/(x^2-3*x+1)^2
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(2 x^{5}-12 x^{4}+24 x^{3}-22 x^{2}+8 x -1\right)}{\left(x -1\right) \left(2 x^{2}-4 x +1\right) \left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(1 - 2*x)*(2*x**5 - 12*x**4 + 24*x**3 - 22*x**2 + 8*x - 1)/((x - 1)*(x**2 - 3*x + 1)**2*(2*x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x^2-4*x+1)*(x^2-3*x+1)^2*F(x)+(2*x-1)*(2*x^5-12*x^4+24*x^3-22*x^2+8*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x^{2}-4 x +1\right) \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)+\left(2 x -1\right) \left(2 x^{5}-12 x^{4}+24 x^{3}-22 x^{2}+8 x -1\right) = 0
Explicit closed form in Maple syntax:
1/20*(5^(1/2)+1)*(((n+39/5)*5^(1/2)-3*n-19)*(3/2-1/2*5^(1/2))^(-n)+(2*n+11/5*5^(1/2)+9)*(3/2+1/2*5^(1/2))^(-n)+5*((2^(1/2)-1)*(1-1/2*2^(1/2))^(-n)+1+(-2^(1/2)-1)*(1+1/2*2^(1/2))^(-n))*(5^(1/2)-1))
Explicit closed form in latex syntax:
\frac{\left(\sqrt{5}+1\right) \left(\left(\left(n +\frac{39}{5}\right) \sqrt{5}-3 n -19\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}+\left(2 n +\frac{11 \sqrt{5}}{5}+9\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}+5 \left(\left(\sqrt{2}-1\right) \left(1-\frac{\sqrt{2}}{2}\right)^{-n}+1+\left(-\sqrt{2}-1\right) \left(1+\frac{\sqrt{2}}{2}\right)^{-n}\right) \left(\sqrt{5}-1\right)\right)}{20}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 86
a(6) = 337
a(n+6) = -2*a(n)+16*a(n+1)-47*a(n+2)+62*a(n+3)-37*a(n+4)+10*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) = 22
a \! \left(5\right) = 86
a \! \left(6\right) = 337
a \! \left(n +6\right) = -2 a \! \left(n \right)+16 a \! \left(n +1\right)-47 a \! \left(n +2\right)+62 a \! \left(n +3\right)-37 a \! \left(n +4\right)+10 a \! \left(n +5\right)-1, \quad n \geq 7
Specification 1
Strategy pack name: regular_insertion_encoding_bottom
Tree: http://permpal.com/tree/14609/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[47,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[17,x]*F[9,x]
F[9,x] = F[10,x]+F[26,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[17,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[18,x]
F[17,x] = x
F[18,x] = F[1,x]+F[15,x]
F[19,x] = F[12,x]
F[20,x] = F[19,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[17,x]*F[23,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[19,x]
F[25,x] = F[21,x]
F[26,x] = F[27,x]+F[6,x]
F[27,x] = 2*F[7,x]+F[28,x]+F[32,x]
F[28,x] = F[17,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[11,x]
F[31,x] = F[27,x]
F[32,x] = F[17,x]*F[33,x]
F[33,x] = F[34,x]+F[41,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[17,x]*F[37,x]
F[37,x] = F[15,x]
F[38,x] = 2*F[7,x]+F[32,x]+F[39,x]
F[39,x] = F[17,x]*F[40,x]
F[40,x] = F[19,x]
F[41,x] = F[38,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[17,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[38,x]
F[46,x] = F[42,x]
F[47,x] = F[17,x]*F[48,x]
F[48,x] = F[49,x]+F[53,x]
F[49,x] = F[15,x]+F[50,x]
F[50,x] = F[47,x]+F[51,x]+F[7,x]
F[51,x] = F[17,x]*F[52,x]
F[52,x] = F[19,x]+F[2,x]
F[53,x] = F[50,x]+F[54,x]
F[54,x] = F[55,x]+F[57,x]+F[67,x]+F[7,x]
F[55,x] = F[17,x]*F[56,x]
F[56,x] = F[11,x]
F[57,x] = F[17,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = 2*F[7,x]+F[32,x]+F[55,x]
F[61,x] = F[54,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[17,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[60,x]
F[66,x] = F[62,x]
F[67,x] = F[17,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[35,x]+F[70,x]
F[70,x] = 2*F[7,x]+F[39,x]+F[67,x]
F[71,x] = F[70,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[17,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[70,x]
F[76,x] = F[72,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_{17}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{47}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{17}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \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) = x
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{17}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{21}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{27}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{32}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{17}\! \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_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)+F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)+F_{67}\! \left(x \right)+F_{7}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{32}\! \left(x \right)+F_{55}\! \left(x \right)
F_{61}\! \left(x \right) = F_{54}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{17}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{60}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{17}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{35}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{7}\! \left(x \right)+F_{39}\! \left(x \right)+F_{67}\! \left(x \right)
F_{71}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_47(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_17(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_26(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_17(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_18(x))
Eq(F_17(x), x)
Eq(F_18(x), F_1(x) + F_15(x))
Eq(F_19(x), F_12(x))
Eq(F_20(x), F_19(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_17(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_21(x))
Eq(F_26(x), F_27(x) + F_6(x))
Eq(F_27(x), F_28(x) + F_32(x) + 2*F_7(x))
Eq(F_28(x), F_17(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_11(x))
Eq(F_31(x), F_27(x))
Eq(F_32(x), F_17(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_41(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_17(x)*F_37(x))
Eq(F_37(x), F_15(x))
Eq(F_38(x), F_32(x) + F_39(x) + 2*F_7(x))
Eq(F_39(x), F_17(x)*F_40(x))
Eq(F_40(x), F_19(x))
Eq(F_41(x), F_38(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_17(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_38(x))
Eq(F_46(x), F_42(x))
Eq(F_47(x), F_17(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_53(x))
Eq(F_49(x), F_15(x) + F_50(x))
Eq(F_50(x), F_47(x) + F_51(x) + F_7(x))
Eq(F_51(x), F_17(x)*F_52(x))
Eq(F_52(x), F_19(x) + F_2(x))
Eq(F_53(x), F_50(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_57(x) + F_67(x) + F_7(x))
Eq(F_55(x), F_17(x)*F_56(x))
Eq(F_56(x), F_11(x))
Eq(F_57(x), F_17(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_32(x) + F_55(x) + 2*F_7(x))
Eq(F_61(x), F_54(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_17(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_60(x))
Eq(F_66(x), F_62(x))
Eq(F_67(x), F_17(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_35(x) + F_70(x))
Eq(F_70(x), F_39(x) + F_67(x) + 2*F_7(x))
Eq(F_71(x), F_70(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_17(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_70(x))
Eq(F_76(x), F_72(x))
Pack JSON:
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Specification JSON:
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Specification 2
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14610/
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[31,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[20,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[17,x]
F[20,x] = F[21,x]+F[22,x]+F[30,x]
F[21,x] = 0
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[24,x]
F[27,x] = F[20,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[12,x]*F[13,x]
F[31,x] = F[32,x]+F[46,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[1,x]+F[14,x]
F[36,x] = F[32,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[32,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[40,x]
F[43,x] = F[37,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[43,x]
F[46,x] = F[132,x]+F[21,x]+F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[80,x]
F[49,x] = F[50,x]+F[6,x]
F[50,x] = F[21,x]+F[22,x]+F[51,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[13,x]+F[53,x]
F[53,x] = F[54,x]+F[65,x]
F[54,x] = F[21,x]+F[55,x]+F[60,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[24,x]+F[57,x]
F[57,x] = F[18,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[57,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[17,x]+F[62,x]
F[62,x] = F[54,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[62,x]
F[65,x] = F[21,x]+F[66,x]+F[74,x]+F[79,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[25,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[12,x]*F[68,x]
F[71,x] = F[28,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[71,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[27,x]+F[76,x]
F[76,x] = F[65,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[76,x]
F[79,x] = F[12,x]*F[53,x]
F[80,x] = F[46,x]+F[81,x]
F[81,x] = 2*F[21,x]+F[100,x]+F[82,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[97,x]
F[84,x] = F[85,x]+F[95,x]
F[85,x] = F[21,x]+F[86,x]+F[93,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[10,x]+F[20,x]
F[89,x] = F[85,x]+F[90,x]
F[90,x] = 2*F[21,x]+F[82,x]+F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[37,x]+F[90,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[32,x]+F[85,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[84,x]
F[97,x] = F[90,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[97,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[92,x]
F[102,x] = F[103,x]+F[117,x]
F[103,x] = 2*F[21,x]+F[104,x]+F[112,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[107,x]+F[41,x]
F[107,x] = F[108,x]
F[108,x] = F[106,x]*F[12,x]
F[109,x] = F[110,x]+F[44,x]
F[110,x] = F[111,x]
F[111,x] = F[109,x]*F[12,x]
F[112,x] = F[113,x]*F[12,x]
F[113,x] = F[114,x]+F[43,x]
F[114,x] = F[103,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[114,x]*F[12,x]
F[117,x] = 2*F[21,x]+F[118,x]+F[126,x]+F[131,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[120,x]+F[123,x]
F[120,x] = F[121,x]+F[95,x]
F[121,x] = F[122,x]
F[122,x] = F[12,x]*F[120,x]
F[123,x] = F[124,x]+F[98,x]
F[124,x] = F[125,x]
F[125,x] = F[12,x]*F[123,x]
F[126,x] = F[12,x]*F[127,x]
F[127,x] = F[128,x]+F[97,x]
F[128,x] = F[117,x]+F[129,x]
F[129,x] = F[130,x]
F[130,x] = F[12,x]*F[128,x]
F[131,x] = F[102,x]*F[12,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[134,x]+F[94,x]
F[134,x] = F[135,x]+F[151,x]
F[135,x] = F[136,x]+F[146,x]+F[21,x]
F[136,x] = F[12,x]*F[137,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[14,x]+F[54,x]
F[139,x] = F[140,x]+F[37,x]
F[140,x] = 2*F[21,x]+F[104,x]+F[141,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[143,x]+F[43,x]
F[143,x] = F[140,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[12,x]*F[143,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[40,x]
F[148,x] = F[135,x]+F[149,x]
F[149,x] = F[150,x]
F[150,x] = F[12,x]*F[148,x]
F[151,x] = F[152,x]+F[164,x]+F[169,x]+F[21,x]
F[152,x] = F[12,x]*F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[20,x]+F[65,x]
F[155,x] = F[156,x]+F[90,x]
F[156,x] = 2*F[21,x]+F[118,x]+F[157,x]+F[162,x]
F[157,x] = F[12,x]*F[158,x]
F[158,x] = F[159,x]+F[97,x]
F[159,x] = F[156,x]+F[160,x]
F[160,x] = F[161,x]
F[161,x] = F[12,x]*F[159,x]
F[162,x] = F[12,x]*F[163,x]
F[163,x] = F[140,x]+F[156,x]
F[164,x] = F[12,x]*F[165,x]
F[165,x] = F[166,x]+F[84,x]
F[166,x] = F[151,x]+F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[12,x]*F[166,x]
F[169,x] = F[12,x]*F[134,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_{31}\! \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_{20}\! \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_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{46}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{132}\! \left(x \right)+F_{21}\! \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_{80}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \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_{54}\! \left(x \right)+F_{65}\! \left(x \right)
F_{54}\! \left(x \right) = F_{21}\! \left(x \right)+F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{24}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{17}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right)+F_{66}\! \left(x \right)+F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{25}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{28}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{27}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{65}\! \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_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{80}\! \left(x \right) = F_{46}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{100}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{97}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{95}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right)+F_{86}\! \left(x \right)+F_{93}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{37}\! \left(x \right)+F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{32}\! \left(x \right)+F_{85}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{97}\! \left(x \right) = F_{90}\! \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_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{92}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{117}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{104}\! \left(x \right)+F_{112}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{41}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{44}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{12}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{43}\! \left(x \right)
F_{114}\! \left(x \right) = F_{103}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{118}\! \left(x \right)+F_{126}\! \left(x \right)+F_{131}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{95}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{98}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{97}\! \left(x \right)
F_{128}\! \left(x \right) = F_{117}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \left(x \right)
F_{131}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{94}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{151}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{146}\! \left(x \right)+F_{21}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{37}\! \left(x \right)
F_{140}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{104}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{43}\! \left(x \right)
F_{143}\! \left(x \right) = F_{140}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{143}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{40}\! \left(x \right)
F_{148}\! \left(x \right) = F_{135}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{148}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{164}\! \left(x \right)+F_{169}\! \left(x \right)+F_{21}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{20}\! \left(x \right)+F_{65}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{90}\! \left(x \right)
F_{156}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{118}\! \left(x \right)+F_{157}\! \left(x \right)+F_{162}\! \left(x \right)
F_{157}\! \left(x \right) = F_{12}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{97}\! \left(x \right)
F_{159}\! \left(x \right) = F_{156}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{12}\! \left(x \right) F_{159}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{140}\! \left(x \right)+F_{156}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{84}\! \left(x \right)
F_{166}\! \left(x \right) = F_{151}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{12}\! \left(x \right) F_{166}\! \left(x \right)
F_{169}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \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_31(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_20(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_9(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_17(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_30(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_24(x))
Eq(F_27(x), F_20(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_12(x)*F_13(x))
Eq(F_31(x), F_32(x) + F_46(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_1(x) + F_14(x))
Eq(F_36(x), F_32(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_32(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_40(x))
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_43(x))
Eq(F_46(x), F_132(x) + F_21(x) + F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_80(x))
Eq(F_49(x), F_50(x) + F_6(x))
Eq(F_50(x), F_21(x) + F_22(x) + F_51(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_13(x) + F_53(x))
Eq(F_53(x), F_54(x) + F_65(x))
Eq(F_54(x), F_21(x) + F_55(x) + F_60(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_24(x) + F_57(x))
Eq(F_57(x), F_18(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_57(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_17(x) + F_62(x))
Eq(F_62(x), F_54(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_62(x))
Eq(F_65(x), F_21(x) + F_66(x) + F_74(x) + F_79(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_25(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_12(x)*F_68(x))
Eq(F_71(x), F_28(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_71(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_27(x) + F_76(x))
Eq(F_76(x), F_65(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_76(x))
Eq(F_79(x), F_12(x)*F_53(x))
Eq(F_80(x), F_46(x) + F_81(x))
Eq(F_81(x), F_100(x) + 2*F_21(x) + F_82(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_97(x))
Eq(F_84(x), F_85(x) + F_95(x))
Eq(F_85(x), F_21(x) + F_86(x) + F_93(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_10(x) + F_20(x))
Eq(F_89(x), F_85(x) + F_90(x))
Eq(F_90(x), 2*F_21(x) + F_82(x) + F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_37(x) + F_90(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_32(x) + F_85(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_84(x))
Eq(F_97(x), F_90(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_12(x)*F_97(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_92(x))
Eq(F_102(x), F_103(x) + F_117(x))
Eq(F_103(x), F_104(x) + F_112(x) + 2*F_21(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_107(x) + F_41(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_106(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_44(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_109(x)*F_12(x))
Eq(F_112(x), F_113(x)*F_12(x))
Eq(F_113(x), F_114(x) + F_43(x))
Eq(F_114(x), F_103(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_114(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_126(x) + F_131(x) + 2*F_21(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_120(x) + F_123(x))
Eq(F_120(x), F_121(x) + F_95(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_12(x)*F_120(x))
Eq(F_123(x), F_124(x) + F_98(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_12(x)*F_123(x))
Eq(F_126(x), F_12(x)*F_127(x))
Eq(F_127(x), F_128(x) + F_97(x))
Eq(F_128(x), F_117(x) + F_129(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_12(x)*F_128(x))
Eq(F_131(x), F_102(x)*F_12(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_134(x) + F_94(x))
Eq(F_134(x), F_135(x) + F_151(x))
Eq(F_135(x), F_136(x) + F_146(x) + F_21(x))
Eq(F_136(x), F_12(x)*F_137(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_14(x) + F_54(x))
Eq(F_139(x), F_140(x) + F_37(x))
Eq(F_140(x), F_104(x) + F_141(x) + 2*F_21(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_143(x) + F_43(x))
Eq(F_143(x), F_140(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_12(x)*F_143(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_40(x))
Eq(F_148(x), F_135(x) + F_149(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_12(x)*F_148(x))
Eq(F_151(x), F_152(x) + F_164(x) + F_169(x) + F_21(x))
Eq(F_152(x), F_12(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_20(x) + F_65(x))
Eq(F_155(x), F_156(x) + F_90(x))
Eq(F_156(x), F_118(x) + F_157(x) + F_162(x) + 2*F_21(x))
Eq(F_157(x), F_12(x)*F_158(x))
Eq(F_158(x), F_159(x) + F_97(x))
Eq(F_159(x), F_156(x) + F_160(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_12(x)*F_159(x))
Eq(F_162(x), F_12(x)*F_163(x))
Eq(F_163(x), F_140(x) + F_156(x))
Eq(F_164(x), F_12(x)*F_165(x))
Eq(F_165(x), F_166(x) + F_84(x))
Eq(F_166(x), F_151(x) + F_167(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_12(x)*F_166(x))
Eq(F_169(x), F_12(x)*F_134(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:
{"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": [2, 1, 3, 0], "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": [2, 1, 3, 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": [2, 1, 3, 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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, 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