0132_0213_0231_3012
Counting sequence:
1, 1, 2, 6, 20, 66, 215, 701, 2308, 7700, 26044, 89247, 309524, 1085247, 3842649, 13726602, 49422035, 179198251, 653836635, 2398999669, 8846155819, 32765207731, 121844281837, 454733959017, 1702623665893, 6393782237159, 24074694386321, 90871540431023, 343773135123669, 1303215439556199, 4949860957232565, 18833983973533392, 71781125421891239, 273999187333127094, 1047408639028717059, 4009331910800134850, 15366735627752617758, 58967530258422092022, 226535740523510317716, 871216778808613908337, 3353952188415481354612, 12924269814819137681477, 49848580401538635611799, 192432261083690836539423, 743469853659614575318447, 2874700387608656570399300, 11123720143745665286746651, 43074605031532976242192088, 166914023586224432853390886, 647220070163267722344886794, 2511232369419837093932247258, 9749592697663072630048972415, 37873917828431765193432751520, 147210346180875378891286961885, 572494735416621745433990121327, 2227567977102197366065675927533, 8671784313026247710226995296879, 33775063790586877705676793687614, 131609333636070833569521073465657, 513065702932583194505668012324172, 2001006043680360480231251880402016, 7807403321467190042714666575375596, 30474852938902675124884844931108252, 119000200700448575014094727737089706, 464857024956380429153915137733639576, 1816567527313119137091800463674291834, 7101321798273989020976396883689660739, 27770111263922394925032870652223052534, 108633136734503119239735989673398133214, 425097926539137620307821772209804336171, 1664000689804239102873574606026776366986, 6515562643410135823253744665405214030660, 25519988869906683202470844359912212719165, 99985161836687677253040454144933709033316, 391844429718275197018878415017099245361276, 1536071831839499211541763689721869152645299, 6023180870074254711184478769839708181154094, 23624017188508966220958562358640082470801434, 92681299457334278464107837853362159798652209, 363695698817265844714363464465892398625217586, 1427542928503062449739238160569484515723530636, 5604572969093805364445544305609432856256083445, 22008765957354952738153431189899002588959100310, 86446265636149831061170641166445558192814537496, 339618874195335732617893264289340306628585833571, 1334535632494177995584637142300972921598836755554, 5245164634547038133191050897622787946720123638734, 20619425651965985061536203982475408884969527689979, 81073787234404046860843582304109026592674738895184, 318837101397093901195715359507106632762932851426806, 1254122159031546829567444065187044210080761357818821, 4933914225982943464482561966578161785180597752332420, 19414327015208042775158777438770925226059444372993260, 76406509947530006077117470405787750482416142748011321, 300755793336120578321426683366991221330485448924612086, 1184054386526729162629009082471509423150467549598578474, 4662316527709156529710034469543109205583545603089937959, 18361273742103295149712136773823718896375806309572584444, 72322485388597986717821613127961406365387676156406351614, 284912792757332299394868008926706082472727513332335579561, 1122579880745523670185311749112191958225463119754866569406
Generating function in Maple syntax:
1/2*((-x^5+6*x^4-15*x^3+14*x^2-6*x+1)*(1-4*x)^(1/2)+x^5-10*x^4+17*x^3-14*x^2+6*x-1)/x/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-x^{5}+6 x^{4}-15 x^{3}+14 x^{2}-6 x +1\right) \sqrt{1-4 x}+x^{5}-10 x^{4}+17 x^{3}-14 x^{2}+6 x -1}{2 x \left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**5/2 - 5*x**4 + 17*x**3/2 - 7*x**2 + 3*x + sqrt(1 - 4*x)*(-x**5 + 6*x**4 - 15*x**3 + 14*x**2 - 6*x + 1)/2 - 1/2)/(x*(x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2-3*x+1)^2*(x-1)^6*F(x)^2-(x^2-3*x+1)*(x^5-10*x^4+17*x^3-14*x^2+6*x-1)*(x-1)^3*F(x)+x^10-12*x^9+64*x^8-191*x^7+365*x^6-450*x^5+362*x^4-190*x^3+63*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}-3 x +1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(x^{2}-3 x +1\right) \left(x^{5}-10 x^{4}+17 x^{3}-14 x^{2}+6 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{10}-12 x^{9}+64 x^{8}-191 x^{7}+365 x^{6}-450 x^{5}+362 x^{4}-190 x^{3}+63 x^{2}-12 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 66
a(6) = 215
a(7) = 701
a(8) = 2308
a(9) = 7700
a(10) = 26044
a(n+9) = 2*(1+2*n)/(n+10)*a(n)-(62+41*n)/(n+10)*a(n+1)+14*(34+13*n)/(n+10)*a(n+2)-(1590+439*n)/(n+10)*a(n+3)+13*(214+47*n)/(n+10)*a(n+4)-2*(1421+256*n)/(n+10)*a(n+5)+4*(437+66*n)/(n+10)*a(n+6)-2*(317+41*n)/(n+10)*a(n+7)+2*(62+7*n)/(n+10)*a(n+8)+2*(n+1)/(n+10), n >= 11
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) = 66
a \! \left(6\right) = 215
a \! \left(7\right) = 701
a \! \left(8\right) = 2308
a \! \left(9\right) = 7700
a \! \left(10\right) = 26044
a \! \left(n +9\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{n +10}-\frac{\left(62+41 n \right) a \! \left(n +1\right)}{n +10}+\frac{14 \left(34+13 n \right) a \! \left(n +2\right)}{n +10}-\frac{\left(1590+439 n \right) a \! \left(n +3\right)}{n +10}+\frac{13 \left(214+47 n \right) a \! \left(n +4\right)}{n +10}-\frac{2 \left(1421+256 n \right) a \! \left(n +5\right)}{n +10}+\frac{4 \left(437+66 n \right) a \! \left(n +6\right)}{n +10}-\frac{2 \left(317+41 n \right) a \! \left(n +7\right)}{n +10}+\frac{2 \left(62+7 n \right) a \! \left(n +8\right)}{n +10}+\frac{2 n +2}{n +10}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21172/
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[9,x]
F[3,x] = F[1,x]+F[100,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[41,x]*F[6,x]*F[9,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[9,x]
F[14,x] = F[15,x]+F[27,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[9,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[1,x]+F[9,x]
F[19,x] = F[15,x]+F[20,x]
F[20,x] = F[21,x]+F[22,x]+F[26,x]
F[21,x] = 0
F[22,x] = F[23,x]*F[9,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[9,x]
F[25,x] = F[20,x]
F[26,x] = F[15,x]*F[9,x]
F[27,x] = F[21,x]+F[28,x]+F[40,x]
F[28,x] = F[29,x]*F[9,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[12,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[9,x]
F[33,x] = F[27,x]+F[34,x]
F[34,x] = 2*F[21,x]+F[35,x]+F[39,x]
F[35,x] = F[36,x]*F[9,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[31,x]
F[38,x] = F[34,x]
F[39,x] = F[27,x]*F[9,x]
F[40,x] = F[14,x]*F[9,x]
F[41,x] = F[1,x]+F[42,x]+F[66,x]
F[42,x] = F[43,x]*F[9,x]
F[43,x] = F[44,x,1]
F[44,x,k[0]] = F[45,x,k[0]]+F[51,x,k[0]]
F[45,x,k[0]] = F[46,x]+F[49,x,k[0]]
F[46,x] = F[1,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[46,x]*F[9,x]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = k[0]*x
F[51,x,k[0]] = F[52,x]+F[59,x,k[0]]
F[52,x] = F[15,x]+F[53,x]
F[53,x] = F[21,x]+F[54,x]+F[58,x]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[47,x]
F[57,x] = F[53,x]
F[58,x] = F[52,x]*F[9,x]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[21,x]+F[61,x,k[0]]+F[65,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]*F[9,x]
F[62,x,k[0]] = F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[50,x,k[0]]
F[64,x,k[0]] = F[60,x,k[0]]
F[65,x,k[0]] = F[15,x]*F[50,x,k[0]]
F[66,x] = F[67,x]*F[9,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = F[1,x]+F[69,x,k[0]]+F[97,x,k[0]]+F[99,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]*F[9,x]
F[70,x,k[0]] = F[71,x,k[0]]+F[80,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[79,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[76,x,k[0]]
F[73,x,k[0]] = F[1,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[50,x,k[0]]*F[73,x,k[0]]
F[76,x,k[0]] = F[47,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[50,x,k[0]]*F[76,x,k[0]]
F[79,x,k[0]] = F[9,x]
F[80,x,k[0]] = F[81,x,k[0]]+F[96,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[89,x,k[0]]
F[82,x,k[0]] = F[15,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[21,x]+F[84,x,k[0]]+F[88,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]*F[9,x]
F[85,x,k[0]] = F[86,x,k[0]]+F[87,x,k[0]]
F[86,x,k[0]] = F[74,x,k[0]]
F[87,x,k[0]] = F[83,x,k[0]]
F[88,x,k[0]] = F[50,x,k[0]]*F[82,x,k[0]]
F[89,x,k[0]] = F[53,x]+F[90,x,k[0]]
F[90,x,k[0]] = 2*F[21,x]+F[91,x,k[0]]+F[95,x,k[0]]
F[91,x,k[0]] = F[9,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]+F[94,x,k[0]]
F[93,x,k[0]] = F[77,x,k[0]]
F[94,x,k[0]] = F[90,x,k[0]]
F[95,x,k[0]] = F[50,x,k[0]]*F[89,x,k[0]]
F[96,x,k[0]] = F[20,x]
F[97,x,k[0]] = F[9,x]*F[98,x,k[0]]
F[98,x,k[0]] = 1/(-1+k[0])*(F[68,x,k[0]]*k[0]-F[68,x,1])
F[99,x,k[0]] = F[50,x,k[0]]*F[68,x,k[0]]
F[100,x] = F[101,x]*F[9,x]
F[101,x] = F[1,x]+F[102,x]+F[137,x]+F[150,x]
F[102,x] = F[103,x]*F[9,x]
F[103,x] = F[104,x]+F[113,x]
F[104,x] = F[105,x]+F[112,x]
F[105,x] = F[1,x]+F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[9,x]
F[108,x] = F[109,x]+F[18,x]
F[109,x] = F[110,x]+F[47,x]
F[110,x] = F[111,x]
F[111,x] = F[47,x]*F[9,x]
F[112,x] = F[9,x]
F[113,x] = F[114,x]+F[133,x]
F[114,x] = F[115,x]+F[47,x]
F[115,x] = F[116,x]+F[118,x]+F[21,x]
F[116,x] = F[117,x]*F[9,x]
F[117,x] = F[106,x]+F[115,x]
F[118,x] = F[119,x]*F[9,x]
F[119,x] = F[120,x]+F[124,x]
F[120,x] = F[121,x]+F[47,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[9,x]
F[123,x] = F[121,x]+F[9,x]
F[124,x] = F[125,x]+F[130,x]
F[125,x] = F[126,x]+F[128,x]+F[21,x]
F[126,x] = F[127,x]*F[9,x]
F[127,x] = F[125,x]+F[47,x]
F[128,x] = F[129,x]*F[9,x]
F[129,x] = F[125,x]+F[47,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[9,x]
F[132,x] = F[110,x]+F[130,x]
F[133,x] = F[134,x]
F[134,x] = F[111,x]+F[135,x]+F[21,x]
F[135,x] = F[136,x]*F[9,x]
F[136,x] = F[134,x]+F[9,x]
F[137,x] = F[138,x]*F[9,x]
F[138,x] = F[139,x]+F[140,x]
F[139,x] = F[129,x]+F[46,x]
F[140,x] = F[129,x]+F[141,x]
F[141,x] = F[142,x]+F[145,x]
F[142,x] = F[135,x]+F[143,x]+F[21,x]
F[143,x] = F[144,x]*F[9,x]
F[144,x] = F[142,x]+F[47,x]
F[145,x] = F[146,x]+F[147,x]+F[149,x]+F[21,x]
F[146,x] = 0
F[147,x] = F[148,x]*F[9,x]
F[148,x] = F[125,x]+F[145,x]
F[149,x] = F[141,x]*F[9,x]
F[150,x] = F[151,x]*F[9,x]
F[151,x] = F[152,x,1]
F[152,x,k[0]] = F[1,x]+F[153,x,k[0]]+F[192,x,k[0]]+F[210,x,k[0]]+F[212,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]*F[9,x]
F[154,x,k[0]] = F[155,x,k[0]]+F[165,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[164,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[73,x,k[0]]
F[157,x,k[0]] = F[106,x]+F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[21,x]+F[78,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]*F[9,x]
F[160,x,k[0]] = F[161,x,k[0]]+F[63,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[47,x]*F[50,x,k[0]]
F[164,x,k[0]] = F[9,x]
F[165,x,k[0]] = F[166,x,k[0]]+F[191,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]+F[172,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[47,x]
F[168,x,k[0]] = F[169,x,k[0]]+F[171,x,k[0]]+F[21,x]
F[169,x,k[0]] = F[170,x,k[0]]*F[9,x]
F[170,x,k[0]] = F[168,x,k[0]]+F[74,x,k[0]]
F[171,x,k[0]] = F[167,x,k[0]]*F[50,x,k[0]]
F[172,x,k[0]] = F[115,x]+F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[176,x,k[0]]+F[186,x,k[0]]+F[21,x]
F[174,x,k[0]] = F[175,x,k[0]]*F[9,x]
F[175,x,k[0]] = F[158,x,k[0]]+F[173,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]*F[9,x]
F[177,x,k[0]] = F[178,x,k[0]]+F[182,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]*F[9,x]
F[181,x,k[0]] = F[179,x,k[0]]+F[50,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]*F[9,x]
F[185,x,k[0]] = F[162,x,k[0]]+F[183,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]*F[50,x,k[0]]
F[187,x,k[0]] = F[125,x]+F[188,x,k[0]]
F[188,x,k[0]] = 2*F[21,x]+F[186,x,k[0]]+F[189,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]*F[9,x]
F[190,x,k[0]] = F[188,x,k[0]]+F[77,x,k[0]]
F[191,x,k[0]] = F[134,x]
F[192,x,k[0]] = F[193,x,k[0]]*F[9,x]
F[193,x,k[0]] = F[194,x,k[0]]+F[196,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]+F[72,x,k[0]]
F[195,x,k[0]] = F[167,x,k[0]]+F[187,x,k[0]]
F[196,x,k[0]] = F[195,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[204,x,k[0]]
F[198,x,k[0]] = F[142,x]+F[199,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[201,x,k[0]]+F[203,x,k[0]]+F[21,x]
F[200,x,k[0]] = 0
F[201,x,k[0]] = F[202,x,k[0]]*F[9,x]
F[202,x,k[0]] = F[168,x,k[0]]+F[199,x,k[0]]
F[203,x,k[0]] = F[198,x,k[0]]*F[50,x,k[0]]
F[204,x,k[0]] = F[145,x]+F[205,x,k[0]]
F[205,x,k[0]] = 2*F[21,x]+F[206,x,k[0]]+F[207,x,k[0]]+F[209,x,k[0]]
F[206,x,k[0]] = 0
F[207,x,k[0]] = F[208,x,k[0]]*F[9,x]
F[208,x,k[0]] = F[188,x,k[0]]+F[205,x,k[0]]
F[209,x,k[0]] = F[204,x,k[0]]*F[50,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]*F[9,x]
F[211,x,k[0]] = 1/(-1+k[0])*(F[152,x,k[0]]*k[0]-F[152,x,1])
F[212,x,k[0]] = F[152,x,k[0]]*F[50,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{41}\! \left(x \right) F_{6}\! \left(x \right) F_{9}\! \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_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \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_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{9}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)+F_{28}\! \left(x \right)+F_{40}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{27}\! \left(x \right) F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{66}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x , 1\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{46}\! \left(x \right) = F_{1}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right) F_{9}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = y x
F_{51}\! \left(x , y\right) = F_{52}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{21}\! \left(x \right)+F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{97}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{47}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{9}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{53}\! \left(x \right)+F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{91}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{20}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = -\frac{-y F_{68}\! \left(x , y\right)+F_{68}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{9}\! \left(x \right)
F_{101}\! \left(x \right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)+F_{137}\! \left(x \right)+F_{150}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{9}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{113}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{112}\! \left(x \right)
F_{105}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{9}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{18}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{47}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{47}\! \left(x \right) F_{9}\! \left(x \right)
F_{112}\! \left(x \right) = F_{9}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{133}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{47}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{21}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{9}\! \left(x \right)
F_{117}\! \left(x \right) = F_{106}\! \left(x \right)+F_{115}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{9}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{124}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{47}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{9}\! \left(x \right)
F_{123}\! \left(x \right) = F_{121}\! \left(x \right)+F_{9}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{130}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)+F_{21}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{9}\! \left(x \right)
F_{127}\! \left(x \right) = F_{125}\! \left(x \right)+F_{47}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{9}\! \left(x \right)
F_{129}\! \left(x \right) = F_{125}\! \left(x \right)+F_{47}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{9}\! \left(x \right)
F_{132}\! \left(x \right) = F_{110}\! \left(x \right)+F_{130}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{111}\! \left(x \right)+F_{135}\! \left(x \right)+F_{21}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{9}\! \left(x \right)
F_{136}\! \left(x \right) = F_{134}\! \left(x \right)+F_{9}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{9}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{140}\! \left(x \right)
F_{139}\! \left(x \right) = F_{129}\! \left(x \right)+F_{46}\! \left(x \right)
F_{140}\! \left(x \right) = F_{129}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{145}\! \left(x \right)
F_{142}\! \left(x \right) = F_{135}\! \left(x \right)+F_{143}\! \left(x \right)+F_{21}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{9}\! \left(x \right)
F_{144}\! \left(x \right) = F_{142}\! \left(x \right)+F_{47}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)+F_{149}\! \left(x \right)+F_{21}\! \left(x \right)
F_{146}\! \left(x \right) = 0
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{9}\! \left(x \right)
F_{148}\! \left(x \right) = F_{125}\! \left(x \right)+F_{145}\! \left(x \right)
F_{149}\! \left(x \right) = F_{141}\! \left(x \right) F_{9}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{9}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x , 1\right)
F_{152}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{106}\! \left(x \right)+F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{21}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{47}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{9}\! \left(x \right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{47}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{170}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{170}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{115}\! \left(x \right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{176}\! \left(x , y\right)+F_{186}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{185}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{125}\! \left(x \right)+F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{186}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{134}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{142}\! \left(x \right)+F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{203}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{200}\! \left(x , y\right) = 0
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{145}\! \left(x \right)+F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = 2 F_{21}\! \left(x \right)+F_{206}\! \left(x , y\right)+F_{207}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = 0
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{208}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{204}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{211}\! \left(x , y\right) = -\frac{-y F_{152}\! \left(x , y\right)+F_{152}\! \left(x , 1\right)}{-1+y}
F_{212}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{50}\! \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_9(x))
Eq(F_3(x), F_1(x) + F_100(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_41(x)*F_6(x)*F_9(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_9(x))
Eq(F_14(x), F_15(x) + F_27(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_9(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_1(x) + F_9(x))
Eq(F_19(x), F_15(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_26(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_23(x)*F_9(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_9(x))
Eq(F_25(x), F_20(x))
Eq(F_26(x), F_15(x)*F_9(x))
Eq(F_27(x), F_21(x) + F_28(x) + F_40(x))
Eq(F_28(x), F_29(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_12(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_9(x))
Eq(F_33(x), F_27(x) + F_34(x))
Eq(F_34(x), 2*F_21(x) + F_35(x) + F_39(x))
Eq(F_35(x), F_36(x)*F_9(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_31(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_27(x)*F_9(x))
Eq(F_40(x), F_14(x)*F_9(x))
Eq(F_41(x), F_1(x) + F_42(x) + F_66(x))
Eq(F_42(x), F_43(x)*F_9(x))
Eq(F_43(x), F_44(x, 1))
Eq(F_44(x, k_0), F_45(x, k_0) + F_51(x, k_0))
Eq(F_45(x, k_0), F_46(x) + F_49(x, k_0))
Eq(F_46(x), F_1(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_46(x)*F_9(x))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), k_0*x)
Eq(F_51(x, k_0), F_52(x) + F_59(x, k_0))
Eq(F_52(x), F_15(x) + F_53(x))
Eq(F_53(x), F_21(x) + F_54(x) + F_58(x))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_47(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_52(x)*F_9(x))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_21(x) + F_61(x, k_0) + F_65(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0)*F_9(x))
Eq(F_62(x, k_0), F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_50(x, k_0))
Eq(F_64(x, k_0), F_60(x, k_0))
Eq(F_65(x, k_0), F_15(x)*F_50(x, k_0))
Eq(F_66(x), F_67(x)*F_9(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), F_1(x) + F_69(x, k_0) + F_97(x, k_0) + F_99(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0)*F_9(x))
Eq(F_70(x, k_0), F_71(x, k_0) + F_80(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_79(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_76(x, k_0))
Eq(F_73(x, k_0), F_1(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_50(x, k_0)*F_73(x, k_0))
Eq(F_76(x, k_0), F_47(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_50(x, k_0)*F_76(x, k_0))
Eq(F_79(x, k_0), F_9(x))
Eq(F_80(x, k_0), F_81(x, k_0) + F_96(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_89(x, k_0))
Eq(F_82(x, k_0), F_15(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_21(x) + F_84(x, k_0) + F_88(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0)*F_9(x))
Eq(F_85(x, k_0), F_86(x, k_0) + F_87(x, k_0))
Eq(F_86(x, k_0), F_74(x, k_0))
Eq(F_87(x, k_0), F_83(x, k_0))
Eq(F_88(x, k_0), F_50(x, k_0)*F_82(x, k_0))
Eq(F_89(x, k_0), F_53(x) + F_90(x, k_0))
Eq(F_90(x, k_0), 2*F_21(x) + F_91(x, k_0) + F_95(x, k_0))
Eq(F_91(x, k_0), F_9(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0) + F_94(x, k_0))
Eq(F_93(x, k_0), F_77(x, k_0))
Eq(F_94(x, k_0), F_90(x, k_0))
Eq(F_95(x, k_0), F_50(x, k_0)*F_89(x, k_0))
Eq(F_96(x, k_0), F_20(x))
Eq(F_97(x, k_0), F_9(x)*F_98(x, k_0))
Eq(F_98(x, k_0), (k_0*F_68(x, k_0) - F_68(x, 1))/(k_0 - 1))
Eq(F_99(x, k_0), F_50(x, k_0)*F_68(x, k_0))
Eq(F_100(x), F_101(x)*F_9(x))
Eq(F_101(x), F_1(x) + F_102(x) + F_137(x) + F_150(x))
Eq(F_102(x), F_103(x)*F_9(x))
Eq(F_103(x), F_104(x) + F_113(x))
Eq(F_104(x), F_105(x) + F_112(x))
Eq(F_105(x), F_1(x) + F_106(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_9(x))
Eq(F_108(x), F_109(x) + F_18(x))
Eq(F_109(x), F_110(x) + F_47(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_47(x)*F_9(x))
Eq(F_112(x), F_9(x))
Eq(F_113(x), F_114(x) + F_133(x))
Eq(F_114(x), F_115(x) + F_47(x))
Eq(F_115(x), F_116(x) + F_118(x) + F_21(x))
Eq(F_116(x), F_117(x)*F_9(x))
Eq(F_117(x), F_106(x) + F_115(x))
Eq(F_118(x), F_119(x)*F_9(x))
Eq(F_119(x), F_120(x) + F_124(x))
Eq(F_120(x), F_121(x) + F_47(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_9(x))
Eq(F_123(x), F_121(x) + F_9(x))
Eq(F_124(x), F_125(x) + F_130(x))
Eq(F_125(x), F_126(x) + F_128(x) + F_21(x))
Eq(F_126(x), F_127(x)*F_9(x))
Eq(F_127(x), F_125(x) + F_47(x))
Eq(F_128(x), F_129(x)*F_9(x))
Eq(F_129(x), F_125(x) + F_47(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_9(x))
Eq(F_132(x), F_110(x) + F_130(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_111(x) + F_135(x) + F_21(x))
Eq(F_135(x), F_136(x)*F_9(x))
Eq(F_136(x), F_134(x) + F_9(x))
Eq(F_137(x), F_138(x)*F_9(x))
Eq(F_138(x), F_139(x) + F_140(x))
Eq(F_139(x), F_129(x) + F_46(x))
Eq(F_140(x), F_129(x) + F_141(x))
Eq(F_141(x), F_142(x) + F_145(x))
Eq(F_142(x), F_135(x) + F_143(x) + F_21(x))
Eq(F_143(x), F_144(x)*F_9(x))
Eq(F_144(x), F_142(x) + F_47(x))
Eq(F_145(x), F_146(x) + F_147(x) + F_149(x) + F_21(x))
Eq(F_146(x), 0)
Eq(F_147(x), F_148(x)*F_9(x))
Eq(F_148(x), F_125(x) + F_145(x))
Eq(F_149(x), F_141(x)*F_9(x))
Eq(F_150(x), F_151(x)*F_9(x))
Eq(F_151(x), F_152(x, 1))
Eq(F_152(x, k_0), F_1(x) + F_153(x, k_0) + F_192(x, k_0) + F_210(x, k_0) + F_212(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0)*F_9(x))
Eq(F_154(x, k_0), F_155(x, k_0) + F_165(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_164(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_73(x, k_0))
Eq(F_157(x, k_0), F_106(x) + F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_21(x) + F_78(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0)*F_9(x))
Eq(F_160(x, k_0), F_161(x, k_0) + F_63(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_47(x)*F_50(x, k_0))
Eq(F_164(x, k_0), F_9(x))
Eq(F_165(x, k_0), F_166(x, k_0) + F_191(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0) + F_172(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_47(x))
Eq(F_168(x, k_0), F_169(x, k_0) + F_171(x, k_0) + F_21(x))
Eq(F_169(x, k_0), F_170(x, k_0)*F_9(x))
Eq(F_170(x, k_0), F_168(x, k_0) + F_74(x, k_0))
Eq(F_171(x, k_0), F_167(x, k_0)*F_50(x, k_0))
Eq(F_172(x, k_0), F_115(x) + F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_176(x, k_0) + F_186(x, k_0) + F_21(x))
Eq(F_174(x, k_0), F_175(x, k_0)*F_9(x))
Eq(F_175(x, k_0), F_158(x, k_0) + F_173(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0)*F_9(x))
Eq(F_177(x, k_0), F_178(x, k_0) + F_182(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0)*F_9(x))
Eq(F_181(x, k_0), F_179(x, k_0) + F_50(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0)*F_9(x))
Eq(F_185(x, k_0), F_162(x, k_0) + F_183(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0)*F_50(x, k_0))
Eq(F_187(x, k_0), F_125(x) + F_188(x, k_0))
Eq(F_188(x, k_0), F_186(x, k_0) + F_189(x, k_0) + 2*F_21(x))
Eq(F_189(x, k_0), F_190(x, k_0)*F_9(x))
Eq(F_190(x, k_0), F_188(x, k_0) + F_77(x, k_0))
Eq(F_191(x, k_0), F_134(x))
Eq(F_192(x, k_0), F_193(x, k_0)*F_9(x))
Eq(F_193(x, k_0), F_194(x, k_0) + F_196(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0) + F_72(x, k_0))
Eq(F_195(x, k_0), F_167(x, k_0) + F_187(x, k_0))
Eq(F_196(x, k_0), F_195(x, k_0) + F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_204(x, k_0))
Eq(F_198(x, k_0), F_142(x) + F_199(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_201(x, k_0) + F_203(x, k_0) + F_21(x))
Eq(F_200(x, k_0), 0)
Eq(F_201(x, k_0), F_202(x, k_0)*F_9(x))
Eq(F_202(x, k_0), F_168(x, k_0) + F_199(x, k_0))
Eq(F_203(x, k_0), F_198(x, k_0)*F_50(x, k_0))
Eq(F_204(x, k_0), F_145(x) + F_205(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_207(x, k_0) + F_209(x, k_0) + 2*F_21(x))
Eq(F_206(x, k_0), 0)
Eq(F_207(x, k_0), F_208(x, k_0)*F_9(x))
Eq(F_208(x, k_0), F_188(x, k_0) + F_205(x, k_0))
Eq(F_209(x, k_0), F_204(x, k_0)*F_50(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0)*F_9(x))
Eq(F_211(x, k_0), (k_0*F_152(x, k_0) - F_152(x, 1))/(k_0 - 1))
Eq(F_212(x, k_0), F_152(x, k_0)*F_50(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "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], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, 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