0132_0231_1023_3012
Counting sequence:
1, 1, 2, 6, 20, 64, 201, 638, 2064, 6822, 23009, 78984, 275192, 970789, 3460426, 12443613, 45083237, 164394500, 602839858, 2221595443, 8223069706, 30556733709, 113949806831, 426293780235, 1599442179451, 6017058723241, 22691426835051, 85766619752555, 324848130691635, 1232772130517171, 4686701548388745, 17847668916948444, 68073523592109467, 260024813628998354, 994609090503526335, 3809393287063268792, 14608065188871894204, 56083295993917257413, 215551554499969933590, 829317051001229461470, 3193881282238648182139, 12311879310332910867223, 47502620150819225510520, 183434093420271760560680, 708915952788066026649373, 2741862841462535663134303, 10612510479720353051755288, 41105324403008630819723944, 159320832131445731619027333, 617915938260542865124878731, 2398043878289122583575326306, 9312043288347273330089511130, 36181190027758504092834777073, 140656937562659045158459501747, 547105279717078301616419716494, 2129136860826916010184644376944, 8289935003146755983001707337261, 32292816496159523593083394916233, 125852183379650839003939009642432, 490691759305919653946277468056662, 1914006690180066362153179766038047, 7468934237257773046441915074075035, 29157376140693003082503470994511014, 113869462003252871250694873452018961, 444866593388269132615862685039311179, 1738645077364437134012758702641807172, 6797447224525536203311662296618597670, 26584585513478296752519288838576322891, 104006063844143352800531768401961466858, 407031403860582000658859384281811122117, 1593432313633039225886826311991069472447, 6239817602028970150404752823591662872831, 24442129029024752184918936409134320116635, 95770438658064659409791874850893894791741, 375358121458705653378536204533714907341803, 1471562730844488232729795161813381720366799, 5770683076602272418030589490694488105372455, 22635397620530355798317561640446721871639243, 88809329314377355897110417633068073058061997, 348526511760232305361558764103797917868884345, 1368097754367477614861829227084818347138819713, 5371553872160562384358063723596505192017526833, 21095107661437359219155057507696720459120238569, 82862906343722931207942056968125195092710644369, 325561371042971016971504591249404130237650815779, 1279374340087445150562273797916351575690765726611, 5028660434616506308144368052331746926046051813339, 19769460321162183655926237807578857287981656668101, 77736169958003368692040261911572216761522090992893, 305728093263394232676218010777615500113082917992687, 1202623166401117987030709279619044134590866009927087, 4731555959202292147893515016648841205140778709251241, 18619020978796610224558269266495517471981116805977705, 73280167195498983017773574480276390078122026794535631, 288463700562606101998188289311928224357003278875666623, 1135715124597709307431389023869546825345207753114921079, 4472183645973709826600922733450988572045006552749472445, 17613284030411442495674840749772822128253985469293212313, 69379328548626548312201810617219459998111531821152458567, 273330118451675855480953892692037218155891893176465458515, 1076988760424864795975632737149470574876682247000534333443
Generating function in Maple syntax:
1/2*((-x^8+3*x^7-2*x^6-x^5+8*x^3-10*x^2+5*x-1)*(1-4*x)^(1/2)-2*x^9+7*x^8-7*x^7+5*x^5+2*x^4-10*x^3+10*x^2-5*x+1)/x/(2*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-x^{8}+3 x^{7}-2 x^{6}-x^{5}+8 x^{3}-10 x^{2}+5 x -1\right) \sqrt{1-4 x}-2 x^{9}+7 x^{8}-7 x^{7}+5 x^{5}+2 x^{4}-10 x^{3}+10 x^{2}-5 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**9 + 7*x**8/2 - 7*x**7/2 + 5*x**5/2 + x**4 - 5*x**3 + 5*x**2 - 5*x/2 + sqrt(1 - 4*x)*(-x**8 + 3*x**7 - 2*x**6 - x**5 + 8*x**3 - 10*x**2 + 5*x - 1)/2 + 1/2)/(x*(x - 1)**3*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^6*F(x)^2+(x^8-3*x^7+2*x^6+x^5-2*x^4-2*x^3+4*x^2-3*x+1)*(2*x-1)^2*(x-1)^3*F(x)+x^17-6*x^16+13*x^15-10*x^14-6*x^13+16*x^12-12*x^11+20*x^10-38*x^9+33*x^8-23*x^7+71*x^6-150*x^5+167*x^4-110*x^3+44*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}+\left(x^{8}-3 x^{7}+2 x^{6}+x^{5}-2 x^{4}-2 x^{3}+4 x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+x^{17}-6 x^{16}+13 x^{15}-10 x^{14}-6 x^{13}+16 x^{12}-12 x^{11}+20 x^{10}-38 x^{9}+33 x^{8}-23 x^{7}+71 x^{6}-150 x^{5}+167 x^{4}-110 x^{3}+44 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 201
a(7) = 638
a(8) = 2064
a(9) = 6822
a(10) = 23009
a(11) = 78984
a(12) = 275192
a(13) = 970789
a(14) = 3460426
a(15) = 12443613
a(16) = 45083237
a(17) = 164394500
a(n+11) = 4*(-7+2*n)/(n+12)*a(n)-2*(-49+19*n)/(n+12)*a(n+1)+(-126+65*n)/(n+12)*a(n+2)-6*(-15+7*n)/(n+12)*a(n+3)+3*(n-12)/(n+12)*a(n+4)-(406+59*n)/(n+12)*a(n+5)+(1302+191*n)/(n+12)*a(n+6)-4*(446+59*n)/(n+12)*a(n+7)+6*(223+26*n)/(n+12)*a(n+8)-(572+59*n)/(n+12)*a(n+9)+2*(65+6*n)/(n+12)*a(n+10)+2*(n+1)/(n+12), n >= 18
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) = 64
a \! \left(6\right) = 201
a \! \left(7\right) = 638
a \! \left(8\right) = 2064
a \! \left(9\right) = 6822
a \! \left(10\right) = 23009
a \! \left(11\right) = 78984
a \! \left(12\right) = 275192
a \! \left(13\right) = 970789
a \! \left(14\right) = 3460426
a \! \left(15\right) = 12443613
a \! \left(16\right) = 45083237
a \! \left(17\right) = 164394500
a \! \left(n +11\right) = \frac{4 \left(-7+2 n \right) a \! \left(n \right)}{n +12}-\frac{2 \left(-49+19 n \right) a \! \left(n +1\right)}{n +12}+\frac{\left(-126+65 n \right) a \! \left(n +2\right)}{n +12}-\frac{6 \left(-15+7 n \right) a \! \left(n +3\right)}{n +12}+\frac{3 \left(n -12\right) a \! \left(n +4\right)}{n +12}-\frac{\left(406+59 n \right) a \! \left(n +5\right)}{n +12}+\frac{\left(1302+191 n \right) a \! \left(n +6\right)}{n +12}-\frac{4 \left(446+59 n \right) a \! \left(n +7\right)}{n +12}+\frac{6 \left(223+26 n \right) a \! \left(n +8\right)}{n +12}-\frac{\left(572+59 n \right) a \! \left(n +9\right)}{n +12}+\frac{2 \left(65+6 n \right) a \! \left(n +10\right)}{n +12}+\frac{2 n +2}{n +12}, \quad n \geq 18
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21222/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[116,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[115,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[21,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[50,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[43,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x]+F[31,x,k[0]]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = x
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[21,x]+F[26,x]
F[30,x] = F[21,x]*F[23,x]
F[31,x,k[0]] = F[27,x]+F[32,x,k[0]]+F[40,x,k[0]]
F[32,x,k[0]] = F[21,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[27,x]+F[37,x,k[0]]+F[39,x,k[0]]
F[37,x,k[0]] = F[21,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]+F[36,x,k[0]]
F[39,x,k[0]] = F[15,x,k[0]]*F[23,x]
F[40,x,k[0]] = F[15,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[23,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[40,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[64,x,k[0]]
F[44,x,k[0]] = F[45,x]+F[58,x,k[0]]
F[45,x] = F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[21,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[1,x]+F[46,x]
F[50,x] = F[51,x]
F[51,x] = F[21,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[1,x]+F[55,x]
F[55,x] = F[21,x]*F[54,x]
F[56,x] = F[20,x]*F[23,x]
F[57,x] = F[25,x]*F[45,x]
F[58,x,k[0]] = F[27,x]+F[59,x,k[0]]+F[63,x,k[0]]
F[59,x,k[0]] = F[21,x]*F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[62,x,k[0]]
F[61,x,k[0]] = F[13,x,k[0]]
F[62,x,k[0]] = F[58,x,k[0]]
F[63,x,k[0]] = F[15,x,k[0]]*F[44,x,k[0]]
F[64,x,k[0]] = F[65,x]+F[89,x,k[0]]
F[65,x] = F[27,x]+F[66,x]+F[73,x]
F[66,x] = F[21,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[70,x]
F[70,x] = F[27,x]+F[66,x]+F[71,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[45,x]+F[70,x]
F[73,x] = F[21,x]*F[74,x]
F[74,x] = F[75,x]+F[81,x]
F[75,x] = F[45,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[21,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[21,x]
F[80,x] = F[76,x]
F[81,x] = F[70,x]+F[82,x]
F[82,x] = 2*F[27,x]+F[83,x]+F[87,x]
F[83,x] = F[21,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[30,x]
F[86,x] = F[83,x]
F[87,x] = F[21,x]*F[88,x]
F[88,x] = F[76,x]+F[82,x]
F[89,x,k[0]] = F[27,x]+F[90,x,k[0]]+F[95,x,k[0]]+F[97,x,k[0]]
F[90,x,k[0]] = F[21,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[93,x,k[0]]
F[92,x,k[0]] = F[42,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = 2*F[27,x]+F[90,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[15,x,k[0]]*F[96,x,k[0]]
F[96,x,k[0]] = F[70,x]+F[94,x,k[0]]
F[97,x,k[0]] = F[21,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[105,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[21,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[104,x,k[0]]
F[103,x,k[0]] = F[15,x,k[0]]
F[104,x,k[0]] = F[100,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = 2*F[27,x]+F[107,x,k[0]]+F[111,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[21,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[110,x,k[0]]
F[109,x,k[0]] = F[39,x,k[0]]
F[110,x,k[0]] = F[107,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[21,x]
F[112,x,k[0]] = F[100,x,k[0]]+F[106,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]*F[21,x]
F[114,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[115,x,k[0]] = F[15,x,k[0]]*F[6,x,k[0]]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[21,x]
F[118,x] = F[119,x]+F[122,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[1,x]+F[17,x]
F[121,x] = F[45,x]+F[65,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[21,x]
F[124,x] = F[125,x]+F[129,x]
F[125,x] = F[126,x]+F[57,x]
F[126,x] = F[1,x]+F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[20,x]*F[21,x]*F[25,x]
F[129,x] = F[55,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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{116}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{21}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{21}\! \left(x \right) F_{54}\! \left(x \right)
F_{56}\! \left(x \right) = F_{20}\! \left(x \right) F_{23}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right) F_{45}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{65}\! \left(x \right) = F_{27}\! \left(x \right)+F_{66}\! \left(x \right)+F_{73}\! \left(x \right)
F_{66}\! \left(x \right) = F_{21}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{27}\! \left(x \right)+F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{45}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{21}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{75}\! \left(x \right) = F_{45}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right)
F_{80}\! \left(x \right) = F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{70}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{30}\! \left(x \right)
F_{86}\! \left(x \right) = F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{21}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{89}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{70}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{100}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{107}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{114}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{115}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{21}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{122}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{121}\! \left(x \right) = F_{45}\! \left(x \right)+F_{65}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{21}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{57}\! \left(x \right)
F_{126}\! \left(x \right) = F_{1}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{20}\! \left(x \right) F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{129}\! \left(x \right) = F_{55}\! \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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_116(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_113(x, k_0) + F_115(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_21(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_50(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_43(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x) + F_31(x, k_0))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_21(x) + F_26(x))
Eq(F_30(x), F_21(x)*F_23(x))
Eq(F_31(x, k_0), F_27(x) + F_32(x, k_0) + F_40(x, k_0))
Eq(F_32(x, k_0), F_21(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_27(x) + F_37(x, k_0) + F_39(x, k_0))
Eq(F_37(x, k_0), F_21(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0) + F_36(x, k_0))
Eq(F_39(x, k_0), F_15(x, k_0)*F_23(x))
Eq(F_40(x, k_0), F_15(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_23(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_40(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_64(x, k_0))
Eq(F_44(x, k_0), F_45(x) + F_58(x, k_0))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_21(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_1(x) + F_46(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_21(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_1(x) + F_55(x))
Eq(F_55(x), F_21(x)*F_54(x))
Eq(F_56(x), F_20(x)*F_23(x))
Eq(F_57(x), F_25(x)*F_45(x))
Eq(F_58(x, k_0), F_27(x) + F_59(x, k_0) + F_63(x, k_0))
Eq(F_59(x, k_0), F_21(x)*F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_62(x, k_0))
Eq(F_61(x, k_0), F_13(x, k_0))
Eq(F_62(x, k_0), F_58(x, k_0))
Eq(F_63(x, k_0), F_15(x, k_0)*F_44(x, k_0))
Eq(F_64(x, k_0), F_65(x) + F_89(x, k_0))
Eq(F_65(x), F_27(x) + F_66(x) + F_73(x))
Eq(F_66(x), F_21(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_23(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_27(x) + F_66(x) + F_71(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_45(x) + F_70(x))
Eq(F_73(x), F_21(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_81(x))
Eq(F_75(x), F_45(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_21(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_21(x))
Eq(F_80(x), F_76(x))
Eq(F_81(x), F_70(x) + F_82(x))
Eq(F_82(x), 2*F_27(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_21(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_30(x))
Eq(F_86(x), F_83(x))
Eq(F_87(x), F_21(x)*F_88(x))
Eq(F_88(x), F_76(x) + F_82(x))
Eq(F_89(x, k_0), F_27(x) + F_90(x, k_0) + F_95(x, k_0) + F_97(x, k_0))
Eq(F_90(x, k_0), F_21(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_93(x, k_0))
Eq(F_92(x, k_0), F_42(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), 2*F_27(x) + F_90(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_15(x, k_0)*F_96(x, k_0))
Eq(F_96(x, k_0), F_70(x) + F_94(x, k_0))
Eq(F_97(x, k_0), F_21(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_105(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_21(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_104(x, k_0))
Eq(F_103(x, k_0), F_15(x, k_0))
Eq(F_104(x, k_0), F_100(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0) + F_111(x, k_0) + 2*F_27(x))
Eq(F_107(x, k_0), F_108(x, k_0)*F_21(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_110(x, k_0))
Eq(F_109(x, k_0), F_39(x, k_0))
Eq(F_110(x, k_0), F_107(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_21(x))
Eq(F_112(x, k_0), F_100(x, k_0) + F_106(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0)*F_21(x))
Eq(F_114(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_115(x, k_0), F_15(x, k_0)*F_6(x, k_0))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_21(x))
Eq(F_118(x), F_119(x) + F_122(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_1(x) + F_17(x))
Eq(F_121(x), F_45(x) + F_65(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_21(x))
Eq(F_124(x), F_125(x) + F_129(x))
Eq(F_125(x), F_126(x) + F_57(x))
Eq(F_126(x), F_1(x) + F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_20(x)*F_21(x)*F_25(x))
Eq(F_129(x), F_55(x))
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:
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{"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 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": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": 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