0123_0132_0231_3012
Counting sequence:
1, 1, 2, 6, 20, 68, 231, 786, 2693, 9320, 32611, 115320, 411721, 1482374, 5376412, 19624128, 72027736, 265661548, 984090668, 3659463854, 13655467692, 51116266614, 191890053574, 722238578494, 2724906099062, 10303483620862, 39039727900582, 148202674783314, 563605252410774, 2146904441479378, 8190738488232483, 31294238870583294, 119728859852796261, 458661093949670176, 1759186971411499519, 6755075432212254736, 25966888497824743261, 99920965256539295734, 384873217645104256409, 1483823255882943214140, 5725727049900326146799, 22112866380965952430946, 85468990118019198059589, 330602068009293080273524, 1279738952840825967408043, 4957267507578918534893450, 19215674865942707574064163, 74533106064329228232168408, 289275592187092526830429749, 1123395621519558810868098826, 4365178602037557736473604663, 16971109128233036086838469848, 66015884045343843421262531345, 256926115637334248066520733698, 1000418431658404796490805811967, 3897276351945123183056557991212, 15189366295211235906190734235801, 59225707994364426786279279834470, 231029042477497167975598231725107, 901576294743792861320854668693576, 3519752735456729561084818247144973, 13746433824081563358926186130503746, 53706997326375993859659201484870852, 209908292900181530125145811812540552, 820694288103762994157784565472433416, 3209827719056059148539004808798601356, 12558163872301863093791091178788017124, 49148524348426149789988436012692232398, 192411364332945467284630213407500557684, 753499571026682272290456577120902939494, 2951641923473369624137539796805656102202, 11565626676924910576368283219508530368606, 45331085646632338081142147805179500918002, 177722031910266892665377911478136285848422, 696949797230867969435341313567157732214570, 2733844435008443368909210253275696030784234, 10726432184249033727120228119939133554295890, 42096229765669877236257709825958528771717250, 165247484594728478691108467322246435574300608, 648825169742078017965222263366388825235829442, 2548116145906873778685694427096967820991793308, 10009377362913590153475373596661066883458108478, 39326827877892371937083385994663717680431521096, 154547706267473815206930083499408896514879331470, 607471434045206538085875656945866758364466115676, 2388233243105363203316705438263604557933059396626, 9391029473634726351805917666354172145284514948764, 36934593536036211753401466104078693359031294254998, 145289836687160779492589280676837994262702817514384, 571632793167836186799687723782621320239902040140394, 2249454840172835006993129522575282222288998847335812, 8853479343743594440319626099930000239881409350068566, 34851831080073825630082937175486769403423766115164792, 137217835056895433952217278338437418954590514513361962, 540340267852800900674947286327977092224920540762386270, 2128111741273641527688971364547960364736706440916849654, 8382825118741384804853436923884650229263725657805472390, 33025840033281437834843945264658940660380483876131169630, 130131811402644227356582464258173102807583021032242441118, 512835285730858377976361088896104568963848110982938093682, 2021323713478695185726969409041551194139182266365093508958
Generating function in Maple syntax:
1/4*((-2*x^5+10*x^4-16*x^3+14*x^2-6*x+1)*(1-4*x)^(1/2)+12*x^5-34*x^4+42*x^3-26*x^2+8*x-1)/x^2/(x-1)^2/(x-1/2)
Generating function in latex syntax:
\frac{\left(-2 x^{5}+10 x^{4}-16 x^{3}+14 x^{2}-6 x +1\right) \sqrt{1-4 x}+12 x^{5}-34 x^{4}+42 x^{3}-26 x^{2}+8 x -1}{4 x^{2} \left(x -1\right)^{2} \left(x -\frac{1}{2}\right)}
Generating function in sympy syntax:
(3*x**5 - 17*x**4/2 + 21*x**3/2 - 13*x**2/2 + 2*x + sqrt(1 - 4*x)*(-2*x**5 + 10*x**4 - 16*x**3 + 14*x**2 - 6*x + 1)/4 - 1/4)/(x**2*(x - 1)**2*(x - 1/2))
Implicit equation for the generating function in Maple syntax:
x^2*(2*x-1)^2*(x-1)^4*F(x)^2-(6*x^4-14*x^3+14*x^2-6*x+1)*(2*x-1)^2*(x-1)^2*F(x)+4*x^9-5*x^8-30*x^7+124*x^6-216*x^5+219*x^4-137*x^3+52*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)^{2}-\left(6 x^{4}-14 x^{3}+14 x^{2}-6 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)+4 x^{9}-5 x^{8}-30 x^{7}+124 x^{6}-216 x^{5}+219 x^{4}-137 x^{3}+52 x^{2}-11 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 68
a(6) = 231
a(7) = 786
a(8) = 2693
a(9) = 9320
a(n+8) = -8*(2*n-1)/(10+n)*a(n)-2*(141*n+299)/(10+n)*a(2+n)+12*(9*n+8)/(10+n)*a(n+1)+6*(68*n+235)/(10+n)*a(n+3)-2*(183*n+878)/(10+n)*a(n+4)+2*(103*n+629)/(10+n)*a(n+5)-14*(5*n+37)/(10+n)*a(n+6)+(113+13*n)/(10+n)*a(n+7)+2/(10+n), n >= 10
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 68
a \! \left(6\right) = 231
a \! \left(7\right) = 786
a \! \left(8\right) = 2693
a \! \left(9\right) = 9320
a \! \left(n +8\right) = -\frac{8 \left(2 n -1\right) a \! \left(n \right)}{10+n}-\frac{2 \left(141 n +299\right) a \! \left(2+n \right)}{10+n}+\frac{12 \left(9 n +8\right) a \! \left(n +1\right)}{10+n}+\frac{6 \left(68 n +235\right) a \! \left(n +3\right)}{10+n}-\frac{2 \left(183 n +878\right) a \! \left(n +4\right)}{10+n}+\frac{2 \left(103 n +629\right) a \! \left(n +5\right)}{10+n}-\frac{14 \left(5 n +37\right) a \! \left(n +6\right)}{10+n}+\frac{\left(113+13 n \right) a \! \left(n +7\right)}{10+n}+\frac{2}{10+n}, \quad n \geq 10
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21133/
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[7,x]
F[3,x] = F[1,x]+F[101,x]+F[4,x]
F[4,x] = F[5,x]*F[7,x]
F[5,x] = F[1,x]+F[17,x]+F[6,x]+F[9,x]
F[6,x] = F[5,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = k[0]*x
F[9,x] = F[10,x]*F[7,x]
F[10,x] = F[1,x]+F[11,x]+F[12,x]+F[17,x]+F[6,x]
F[11,x] = F[10,x]*F[7,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]*F[7,x]
F[14,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[15,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[16,x,k[0]]+F[17,x]+F[6,x]
F[16,x,k[0]] = F[15,x,k[0]]*F[8,x,k[0]]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = F[19,x,k[0]]*F[7,x]
F[19,x,k[0]] = F[1,x]+F[20,x,k[0]]+F[34,x,k[0]]+F[51,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[8,x,k[0]]
F[21,x,k[0]] = F[22,x]+F[25,x,k[0]]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[7,x]
F[25,x,k[0]] = F[26,x,k[0]]+F[29,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[8,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[31,x,k[0]]+F[33,x,k[0]]
F[30,x] = 0
F[31,x,k[0]] = F[32,x,k[0]]*F[8,x,k[0]]
F[32,x,k[0]] = F[23,x]+F[29,x,k[0]]
F[33,x,k[0]] = F[25,x,k[0]]*F[7,x]
F[34,x,k[0]] = F[35,x,k[0]]*F[7,x]
F[35,x,k[0]] = F[36,x]+F[42,x,k[0]]
F[36,x] = F[22,x]+F[37,x]
F[37,x] = F[23,x]+F[38,x]
F[38,x] = F[30,x]+F[39,x]+F[41,x]
F[39,x] = F[40,x]*F[7,x]
F[40,x] = F[23,x]+F[38,x]
F[41,x] = F[37,x]*F[7,x]
F[42,x,k[0]] = F[25,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]*F[7,x]
F[46,x,k[0]] = F[26,x,k[0]]+F[44,x,k[0]]
F[47,x,k[0]] = 2*F[30,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[7,x]
F[49,x,k[0]] = F[29,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[43,x,k[0]]*F[7,x]
F[51,x,k[0]] = F[52,x,k[0]]*F[7,x]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[54,x]+F[77,x,k[0]]+F[79,x,k[0]]
F[53,x,k[0]] = F[52,x,k[0]]*F[8,x,k[0]]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[56,x,k[0]]*F[7,x]
F[56,x,k[0]] = F[1,x]+F[57,x,k[0]]+F[74,x,k[0]]+F[76,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]*F[7,x]
F[58,x,k[0]] = F[59,x,k[0]]+F[63,x,k[0]]
F[59,x,k[0]] = F[28,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[23,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[60,x,k[0]]*F[8,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[69,x,k[0]]
F[64,x,k[0]] = F[23,x]+F[65,x,k[0]]
F[65,x,k[0]] = F[30,x]+F[66,x,k[0]]+F[68,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]*F[7,x]
F[67,x,k[0]] = F[26,x,k[0]]+F[65,x,k[0]]
F[68,x,k[0]] = F[64,x,k[0]]*F[8,x,k[0]]
F[69,x,k[0]] = F[38,x]+F[70,x,k[0]]
F[70,x,k[0]] = 2*F[30,x]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[7,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[61,x,k[0]]+F[70,x,k[0]]
F[73,x,k[0]] = F[69,x,k[0]]*F[8,x,k[0]]
F[74,x,k[0]] = F[7,x]*F[75,x,k[0]]
F[75,x,k[0]] = 1/(-1+k[0])*(F[56,x,k[0]]*k[0]-F[56,x,1])
F[76,x,k[0]] = F[56,x,k[0]]*F[8,x,k[0]]
F[77,x,k[0]] = F[7,x]*F[78,x,k[0]]
F[78,x,k[0]] = (F[52,x,k[0]]*k[0]-F[52,x,1])/(-1+k[0])
F[79,x,k[0]] = F[7,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[81,x]+F[91,x,k[0]]
F[81,x] = F[36,x]+F[82,x]
F[82,x] = F[37,x]+F[83,x]
F[83,x] = F[84,x]+F[87,x]
F[84,x] = F[85,x]
F[85,x] = F[7,x]*F[86,x]
F[86,x] = F[23,x]+F[84,x]
F[87,x] = 2*F[30,x]+F[88,x]+F[90,x]
F[88,x] = F[7,x]*F[89,x]
F[89,x] = F[38,x]+F[87,x]
F[90,x] = F[7,x]*F[83,x]
F[91,x,k[0]] = F[42,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[43,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]
F[95,x,k[0]] = F[7,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[44,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = 3*F[30,x]+F[100,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[7,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[47,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = F[7,x]*F[93,x,k[0]]
F[101,x] = F[102,x]*F[7,x]
F[102,x] = F[1,x]+F[103,x]+F[135,x]+F[146,x]
F[103,x] = F[104,x]*F[7,x]
F[104,x] = F[105,x]+F[117,x]
F[105,x] = F[106,x]+F[116,x]
F[106,x] = F[1,x]+F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[7,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[1,x]+F[7,x]
F[111,x] = F[112,x]+F[23,x]
F[112,x] = F[113,x]+F[115,x]+F[30,x]
F[113,x] = F[114,x]*F[7,x]
F[114,x] = F[112,x]+F[7,x]
F[115,x] = F[23,x]*F[7,x]
F[116,x] = F[23,x]
F[117,x] = F[118,x]+F[134,x]
F[118,x] = F[119,x]+F[23,x]
F[119,x] = F[120,x]+F[122,x]+F[30,x]
F[120,x] = F[121,x]*F[7,x]
F[121,x] = F[107,x]+F[119,x]
F[122,x] = F[123,x]*F[7,x]
F[123,x] = F[124,x]+F[128,x]
F[124,x] = F[125,x]+F[23,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[7,x]
F[127,x] = F[125,x]+F[7,x]
F[128,x] = F[129,x]+F[38,x]
F[129,x] = 2*F[30,x]+F[130,x]+F[132,x]
F[130,x] = F[131,x]*F[7,x]
F[131,x] = F[112,x]+F[129,x]
F[132,x] = F[133,x]*F[7,x]
F[133,x] = F[125,x]+F[129,x]
F[134,x] = F[38,x]
F[135,x] = F[136,x]*F[7,x]
F[136,x] = F[137,x,1]
F[137,x,k[0]] = F[138,x,k[0]]+F[139,x,k[0]]
F[138,x,k[0]] = F[28,x,k[0]]+F[64,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]+F[64,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[38,x]
F[141,x,k[0]] = F[142,x,k[0]]+F[143,x,k[0]]+F[145,x,k[0]]+F[30,x]
F[142,x,k[0]] = 0
F[143,x,k[0]] = F[144,x,k[0]]*F[7,x]
F[144,x,k[0]] = F[141,x,k[0]]+F[65,x,k[0]]
F[145,x,k[0]] = F[140,x,k[0]]*F[8,x,k[0]]
F[146,x] = F[147,x]*F[7,x]
F[147,x] = F[148,x,1]
F[148,x,k[0]] = F[1,x]+F[149,x,k[0]]+F[183,x,k[0]]+F[199,x,k[0]]+F[201,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[7,x]
F[150,x,k[0]] = F[151,x,k[0]]+F[164,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]+F[163,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]+F[28,x,k[0]]
F[153,x,k[0]] = F[107,x]+F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[30,x]+F[62,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[7,x]
F[156,x,k[0]] = F[157,x,k[0]]+F[158,x,k[0]]
F[157,x,k[0]] = F[8,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]+F[162,x,k[0]]+F[30,x]
F[160,x,k[0]] = F[161,x,k[0]]*F[7,x]
F[161,x,k[0]] = F[159,x,k[0]]+F[8,x,k[0]]
F[162,x,k[0]] = F[23,x]*F[8,x,k[0]]
F[163,x,k[0]] = F[23,x]
F[164,x,k[0]] = F[165,x,k[0]]+F[182,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[64,x,k[0]]
F[166,x,k[0]] = F[119,x]+F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[170,x,k[0]]+F[30,x]+F[73,x,k[0]]
F[168,x,k[0]] = F[169,x,k[0]]*F[7,x]
F[169,x,k[0]] = F[154,x,k[0]]+F[167,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]*F[7,x]
F[171,x,k[0]] = F[172,x,k[0]]+F[176,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[7,x]
F[175,x,k[0]] = F[173,x,k[0]]+F[8,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]
F[177,x,k[0]] = 2*F[30,x]+F[178,x,k[0]]+F[180,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]*F[7,x]
F[179,x,k[0]] = F[159,x,k[0]]+F[177,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]*F[7,x]
F[181,x,k[0]] = F[173,x,k[0]]+F[177,x,k[0]]
F[182,x,k[0]] = F[38,x]
F[183,x,k[0]] = F[184,x,k[0]]*F[7,x]
F[184,x,k[0]] = F[185,x,k[0]]+F[58,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]+F[63,x,k[0]]
F[186,x,k[0]] = F[140,x,k[0]]+F[187,x,k[0]]
F[187,x,k[0]] = F[188,x]+F[194,x,k[0]]
F[188,x] = F[189,x]+F[190,x]+F[192,x]+F[30,x]
F[189,x] = 0
F[190,x] = F[191,x]*F[7,x]
F[191,x] = F[188,x]+F[38,x]
F[192,x] = F[193,x]*F[7,x]
F[193,x] = F[188,x]+F[38,x]
F[194,x,k[0]] = 2*F[30,x]+F[195,x,k[0]]+F[196,x,k[0]]+F[198,x,k[0]]
F[195,x,k[0]] = 0
F[196,x,k[0]] = F[197,x,k[0]]*F[7,x]
F[197,x,k[0]] = F[194,x,k[0]]+F[70,x,k[0]]
F[198,x,k[0]] = F[187,x,k[0]]*F[8,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]*F[7,x]
F[200,x,k[0]] = 1/(-1+k[0])*(F[148,x,k[0]]*k[0]-F[148,x,1])
F[201,x,k[0]] = F[148,x,k[0]]*F[8,x,k[0]]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{7}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)+F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{6}\! \left(x \right) = F_{5}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{12}\! \left(x \right)+F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{10}\! \left(x \right) F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{22}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{30}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right) F_{7}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{66}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{69}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{-y F_{56}\! \left(x , y\right)+F_{56}\! \left(x , 1\right)}{-1+y}
F_{76}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}
F_{79}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x \right)+F_{91}\! \left(x , y\right)
F_{81}\! \left(x \right) = F_{36}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{37}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{23}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{7}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{38}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{7}\! \left(x \right) F_{83}\! \left(x \right)
F_{91}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{7}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)+F_{135}\! \left(x \right)+F_{146}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{7}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{117}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{116}\! \left(x \right)
F_{106}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{7}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{23}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{115}\! \left(x \right)+F_{30}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{7}\! \left(x \right)
F_{114}\! \left(x \right) = F_{112}\! \left(x \right)+F_{7}\! \left(x \right)
F_{115}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{116}\! \left(x \right) = F_{23}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{134}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{122}\! \left(x \right)+F_{30}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{7}\! \left(x \right)
F_{121}\! \left(x \right) = F_{107}\! \left(x \right)+F_{119}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{7}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{128}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{23}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{7}\! \left(x \right)
F_{127}\! \left(x \right) = F_{125}\! \left(x \right)+F_{7}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{38}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{7}\! \left(x \right)
F_{131}\! \left(x \right) = F_{112}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{7}\! \left(x \right)
F_{133}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)
F_{134}\! \left(x \right) = F_{38}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{7}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x , 1\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{142}\! \left(x , y\right) = 0
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{7}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x , 1\right)
F_{148}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{107}\! \left(x \right)+F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{162}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{23}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{119}\! \left(x \right)+F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{178}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{38}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x \right)+F_{194}\! \left(x , y\right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)+F_{190}\! \left(x \right)+F_{192}\! \left(x \right)+F_{30}\! \left(x \right)
F_{189}\! \left(x \right) = 0
F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{7}\! \left(x \right)
F_{191}\! \left(x \right) = F_{188}\! \left(x \right)+F_{38}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{7}\! \left(x \right)
F_{193}\! \left(x \right) = F_{188}\! \left(x \right)+F_{38}\! \left(x \right)
F_{194}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{196}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = 0
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{200}\! \left(x , y\right) = -\frac{-y F_{148}\! \left(x , y\right)+F_{148}\! \left(x , 1\right)}{-1+y}
F_{201}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{8}\! \left(x , y\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)*F_7(x))
Eq(F_3(x), F_1(x) + F_101(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_7(x))
Eq(F_5(x), F_1(x) + F_17(x) + F_6(x) + F_9(x))
Eq(F_6(x), F_5(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x), F_10(x)*F_7(x))
Eq(F_10(x), F_1(x) + F_11(x) + F_12(x) + F_17(x) + F_6(x))
Eq(F_11(x), F_10(x)*F_7(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0)*F_7(x))
Eq(F_14(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_15(x, k_0), F_1(x) + F_13(x, k_0) + F_16(x, k_0) + F_17(x) + F_6(x))
Eq(F_16(x, k_0), F_15(x, k_0)*F_8(x, k_0))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), F_19(x, k_0)*F_7(x))
Eq(F_19(x, k_0), F_1(x) + F_20(x, k_0) + F_34(x, k_0) + F_51(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_8(x, k_0))
Eq(F_21(x, k_0), F_22(x) + F_25(x, k_0))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_7(x))
Eq(F_25(x, k_0), F_26(x, k_0) + F_29(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_8(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_31(x, k_0) + F_33(x, k_0))
Eq(F_30(x), 0)
Eq(F_31(x, k_0), F_32(x, k_0)*F_8(x, k_0))
Eq(F_32(x, k_0), F_23(x) + F_29(x, k_0))
Eq(F_33(x, k_0), F_25(x, k_0)*F_7(x))
Eq(F_34(x, k_0), F_35(x, k_0)*F_7(x))
Eq(F_35(x, k_0), F_36(x) + F_42(x, k_0))
Eq(F_36(x), F_22(x) + F_37(x))
Eq(F_37(x), F_23(x) + F_38(x))
Eq(F_38(x), F_30(x) + F_39(x) + F_41(x))
Eq(F_39(x), F_40(x)*F_7(x))
Eq(F_40(x), F_23(x) + F_38(x))
Eq(F_41(x), F_37(x)*F_7(x))
Eq(F_42(x, k_0), F_25(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_7(x))
Eq(F_46(x, k_0), F_26(x, k_0) + F_44(x, k_0))
Eq(F_47(x, k_0), 2*F_30(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_7(x))
Eq(F_49(x, k_0), F_29(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_43(x, k_0)*F_7(x))
Eq(F_51(x, k_0), F_52(x, k_0)*F_7(x))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0) + F_54(x) + F_77(x, k_0) + F_79(x, k_0))
Eq(F_53(x, k_0), F_52(x, k_0)*F_8(x, k_0))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_56(x, k_0)*F_7(x))
Eq(F_56(x, k_0), F_1(x) + F_57(x, k_0) + F_74(x, k_0) + F_76(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0)*F_7(x))
Eq(F_58(x, k_0), F_59(x, k_0) + F_63(x, k_0))
Eq(F_59(x, k_0), F_28(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_23(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_60(x, k_0)*F_8(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_69(x, k_0))
Eq(F_64(x, k_0), F_23(x) + F_65(x, k_0))
Eq(F_65(x, k_0), F_30(x) + F_66(x, k_0) + F_68(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0)*F_7(x))
Eq(F_67(x, k_0), F_26(x, k_0) + F_65(x, k_0))
Eq(F_68(x, k_0), F_64(x, k_0)*F_8(x, k_0))
Eq(F_69(x, k_0), F_38(x) + F_70(x, k_0))
Eq(F_70(x, k_0), 2*F_30(x) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_7(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_61(x, k_0) + F_70(x, k_0))
Eq(F_73(x, k_0), F_69(x, k_0)*F_8(x, k_0))
Eq(F_74(x, k_0), F_7(x)*F_75(x, k_0))
Eq(F_75(x, k_0), (k_0*F_56(x, k_0) - F_56(x, 1))/(k_0 - 1))
Eq(F_76(x, k_0), F_56(x, k_0)*F_8(x, k_0))
Eq(F_77(x, k_0), F_7(x)*F_78(x, k_0))
Eq(F_78(x, k_0), (-k_0*F_52(x, k_0) + F_52(x, 1))/(1 - k_0))
Eq(F_79(x, k_0), F_7(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x) + F_91(x, k_0))
Eq(F_81(x), F_36(x) + F_82(x))
Eq(F_82(x), F_37(x) + F_83(x))
Eq(F_83(x), F_84(x) + F_87(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_7(x)*F_86(x))
Eq(F_86(x), F_23(x) + F_84(x))
Eq(F_87(x), 2*F_30(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_7(x)*F_89(x))
Eq(F_89(x), F_38(x) + F_87(x))
Eq(F_90(x), F_7(x)*F_83(x))
Eq(F_91(x, k_0), F_42(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_43(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0))
Eq(F_95(x, k_0), F_7(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_44(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), F_100(x, k_0) + 3*F_30(x) + F_98(x, k_0))
Eq(F_98(x, k_0), F_7(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_47(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_7(x)*F_93(x, k_0))
Eq(F_101(x), F_102(x)*F_7(x))
Eq(F_102(x), F_1(x) + F_103(x) + F_135(x) + F_146(x))
Eq(F_103(x), F_104(x)*F_7(x))
Eq(F_104(x), F_105(x) + F_117(x))
Eq(F_105(x), F_106(x) + F_116(x))
Eq(F_106(x), F_1(x) + F_107(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_7(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_1(x) + F_7(x))
Eq(F_111(x), F_112(x) + F_23(x))
Eq(F_112(x), F_113(x) + F_115(x) + F_30(x))
Eq(F_113(x), F_114(x)*F_7(x))
Eq(F_114(x), F_112(x) + F_7(x))
Eq(F_115(x), F_23(x)*F_7(x))
Eq(F_116(x), F_23(x))
Eq(F_117(x), F_118(x) + F_134(x))
Eq(F_118(x), F_119(x) + F_23(x))
Eq(F_119(x), F_120(x) + F_122(x) + F_30(x))
Eq(F_120(x), F_121(x)*F_7(x))
Eq(F_121(x), F_107(x) + F_119(x))
Eq(F_122(x), F_123(x)*F_7(x))
Eq(F_123(x), F_124(x) + F_128(x))
Eq(F_124(x), F_125(x) + F_23(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_7(x))
Eq(F_127(x), F_125(x) + F_7(x))
Eq(F_128(x), F_129(x) + F_38(x))
Eq(F_129(x), F_130(x) + F_132(x) + 2*F_30(x))
Eq(F_130(x), F_131(x)*F_7(x))
Eq(F_131(x), F_112(x) + F_129(x))
Eq(F_132(x), F_133(x)*F_7(x))
Eq(F_133(x), F_125(x) + F_129(x))
Eq(F_134(x), F_38(x))
Eq(F_135(x), F_136(x)*F_7(x))
Eq(F_136(x), F_137(x, 1))
Eq(F_137(x, k_0), F_138(x, k_0) + F_139(x, k_0))
Eq(F_138(x, k_0), F_28(x, k_0) + F_64(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0) + F_64(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_38(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_143(x, k_0) + F_145(x, k_0) + F_30(x))
Eq(F_142(x, k_0), 0)
Eq(F_143(x, k_0), F_144(x, k_0)*F_7(x))
Eq(F_144(x, k_0), F_141(x, k_0) + F_65(x, k_0))
Eq(F_145(x, k_0), F_140(x, k_0)*F_8(x, k_0))
Eq(F_146(x), F_147(x)*F_7(x))
Eq(F_147(x), F_148(x, 1))
Eq(F_148(x, k_0), F_1(x) + F_149(x, k_0) + F_183(x, k_0) + F_199(x, k_0) + F_201(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_7(x))
Eq(F_150(x, k_0), F_151(x, k_0) + F_164(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0) + F_163(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_28(x, k_0))
Eq(F_153(x, k_0), F_107(x) + F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_30(x) + F_62(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_7(x))
Eq(F_156(x, k_0), F_157(x, k_0) + F_158(x, k_0))
Eq(F_157(x, k_0), F_8(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0) + F_162(x, k_0) + F_30(x))
Eq(F_160(x, k_0), F_161(x, k_0)*F_7(x))
Eq(F_161(x, k_0), F_159(x, k_0) + F_8(x, k_0))
Eq(F_162(x, k_0), F_23(x)*F_8(x, k_0))
Eq(F_163(x, k_0), F_23(x))
Eq(F_164(x, k_0), F_165(x, k_0) + F_182(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_64(x, k_0))
Eq(F_166(x, k_0), F_119(x) + F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_170(x, k_0) + F_30(x) + F_73(x, k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_7(x))
Eq(F_169(x, k_0), F_154(x, k_0) + F_167(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0)*F_7(x))
Eq(F_171(x, k_0), F_172(x, k_0) + F_176(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_7(x))
Eq(F_175(x, k_0), F_173(x, k_0) + F_8(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0) + F_180(x, k_0) + 2*F_30(x))
Eq(F_178(x, k_0), F_179(x, k_0)*F_7(x))
Eq(F_179(x, k_0), F_159(x, k_0) + F_177(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0)*F_7(x))
Eq(F_181(x, k_0), F_173(x, k_0) + F_177(x, k_0))
Eq(F_182(x, k_0), F_38(x))
Eq(F_183(x, k_0), F_184(x, k_0)*F_7(x))
Eq(F_184(x, k_0), F_185(x, k_0) + F_58(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0) + F_63(x, k_0))
Eq(F_186(x, k_0), F_140(x, k_0) + F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x) + F_194(x, k_0))
Eq(F_188(x), F_189(x) + F_190(x) + F_192(x) + F_30(x))
Eq(F_189(x), 0)
Eq(F_190(x), F_191(x)*F_7(x))
Eq(F_191(x), F_188(x) + F_38(x))
Eq(F_192(x), F_193(x)*F_7(x))
Eq(F_193(x), F_188(x) + F_38(x))
Eq(F_194(x, k_0), F_195(x, k_0) + F_196(x, k_0) + F_198(x, k_0) + 2*F_30(x))
Eq(F_195(x, k_0), 0)
Eq(F_196(x, k_0), F_197(x, k_0)*F_7(x))
Eq(F_197(x, k_0), F_194(x, k_0) + F_70(x, k_0))
Eq(F_198(x, k_0), F_187(x, k_0)*F_8(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0)*F_7(x))
Eq(F_200(x, k_0), (k_0*F_148(x, k_0) - F_148(x, 1))/(k_0 - 1))
Eq(F_201(x, k_0), F_148(x, k_0)*F_8(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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": [3, 0, 1, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, 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