0123_0213_0231_1320_3021
Counting sequence:
1, 1, 2, 6, 19, 55, 148, 387, 997, 2545, 6458, 16328, 41208, 103961, 262475, 663743, 1682152, 4274158, 10890454, 27827847, 71306929, 183209341, 471898550, 1218264980, 3151570164, 8167763765, 21201774743, 55111453307, 143425844932, 373639354810, 974203885138, 2541909092643, 6636390343933, 17334915466681, 45299368143890, 118416354770528, 309637774167792, 809835542769233, 2118468694801379, 5542611309167927, 14503120350253984, 37953589961799046, 99329955586018510, 259978071399461055, 680482075382728009, 1781211968539451125, 4662617268561270638, 12205517235772401452, 31951588080942259692, 83644347583241007725, 218971233608688957743, 573248049105526077683, 1500728546214685258108, 3928845265746168601426, 10285615285089703878730, 26927601739480944035163, 70496361833971645476757, 184559765639176150550833, 483179372736251556113354, 1264970971169789257546232, 3311718255555980921061864, 8670152162214370855275401, 22698672802791745206198395, 59425730994056855572583855, 155578240740029142427017304, 407308414188817515981556510, 1066345810858509146644725958, 2791726561510983606761715447, 7308828807737350431154807777, 19134749420843921967096493165, 50095397945890825524797487398, 131151400126196033630662538948, 343358711268888063094586043108, 898924546113974414174374758821, 2353414541314723110014394839495, 6161318284767773698947766684523, 16130538683181865586442600837172, 42230294416619986705801579316458, 110560337690912495472758705970754, 289450704540964082415104994858387, 757791746964983745850152537793069, 1983924476927727334703737249370281, 5193981561943364068361255535251330, 13598019959032509528781361809300880, 35600077803022964183735545757747424, 93202212400688771596927151818980545, 244006557249573243332235237071613203, 638817454946332049182913734290672167, 1672445798578089844809060097540567312, 4378519922344565181203483869013608630, 11463113930717777313711127191872268478, 30010821792611599622618137126565622063, 78569351289240980919029631004595661433, 205697231752318477890807849207274720741, 538522343307892411814286230095995289310, 1409869796822932569760450376646840086108, 3691087044405869740037451098056524008412, 9663391330767001231760564187831313216733, 25299086936402098630518770993273946346079, 66233869454972903275102080301002727031267, 173402521380613283434600394792237723775724
Generating function in Maple syntax:
(8*x^10-31*x^9+26*x^8+4*x^7-23*x^6+59*x^5-99*x^4+87*x^3-41*x^2+10*x-1)/(x^2-3*x+1)/(x-1)^2/(2*x-1)^3
Generating function in latex syntax:
\frac{8 x^{10}-31 x^{9}+26 x^{8}+4 x^{7}-23 x^{6}+59 x^{5}-99 x^{4}+87 x^{3}-41 x^{2}+10 x -1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{2} \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(8*x**10 - 31*x**9 + 26*x**8 + 4*x**7 - 23*x**6 + 59*x**5 - 99*x**4 + 87*x**3 - 41*x**2 + 10*x - 1)/((x - 1)**2*(2*x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x-1)^2*(2*x-1)^3*F(x)+8*x^10-31*x^9+26*x^8+4*x^7-23*x^6+59*x^5-99*x^4+87*x^3-41*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x -1\right)^{2} \left(2 x -1\right)^{3} F \! \left(x \right)+8 x^{10}-31 x^{9}+26 x^{8}+4 x^{7}-23 x^{6}+59 x^{5}-99 x^{4}+87 x^{3}-41 x^{2}+10 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,41/8,n = 1,65/16,n = 2,21/8,n = 3,1,0)+1/320*(-32*5^(1/2)+160)*(3/2-1/2*5^(1/2))^(-n)+1/320*(32*5^(1/2)+160)*(3/2+1/2*5^(1/2))^(-n)+1/320*(5*n^2+25*n-40)*2^n+n-5
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{41}{8} & n =0 \\ \frac{65}{16} & n =1 \\ \frac{21}{8} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-32 \sqrt{5}+160\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{320}+\frac{\left(32 \sqrt{5}+160\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{320}+\frac{\left(5 n^{2}+25 n -40\right) 2^{n}}{320}+n -5
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 148
a(7) = 387
a(8) = 997
a(9) = 2545
a(10) = 6458
a(n+5) = 8*a(n)-36*a(n+1)+50*a(n+2)-31*a(n+3)+9*a(n+4)+n-7, 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) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 148
a \! \left(7\right) = 387
a \! \left(8\right) = 997
a \! \left(9\right) = 2545
a \! \left(10\right) = 6458
a \! \left(n +5\right) = 8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)+n -7, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16757/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[18,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]+F[56,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[16,x]*F[4,x]
F[25,x] = F[19,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[54,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[34,x]
F[30,x] = F[23,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[4,x]
F[34,x] = F[26,x]+F[35,x]
F[35,x] = 2*F[27,x]+F[36,x]+F[40,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[31,x]
F[39,x] = F[35,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[27,x]+F[43,x]+F[53,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[4,x]+F[46,x]
F[46,x] = F[32,x]
F[47,x] = F[42,x]+F[48,x]
F[48,x] = 2*F[27,x]+F[40,x]+F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[46,x]
F[52,x] = F[48,x]
F[53,x] = F[19,x]*F[4,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[19,x]+F[42,x]
F[56,x] = F[167,x]+F[27,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[70,x]
F[59,x] = F[60,x]+F[7,x]
F[60,x] = F[27,x]+F[61,x]+F[66,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[4,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[32,x]
F[70,x] = F[56,x]+F[71,x]
F[71,x] = F[123,x]+F[163,x]+F[27,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[80,x]
F[74,x] = F[60,x]+F[75,x]
F[75,x] = 2*F[27,x]+F[76,x]+F[78,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[63,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[31,x]
F[80,x] = F[71,x]+F[81,x]
F[81,x] = 2*F[27,x]+F[118,x]+F[82,x]+F[86,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[75,x]
F[85,x] = F[81,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = 2*F[27,x]+F[106,x]+F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]+F[95,x]
F[91,x] = F[63,x]+F[92,x]
F[92,x] = 2*F[27,x]+F[76,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[46,x]
F[95,x] = F[88,x]+F[96,x]
F[96,x] = 2*F[27,x]+F[101,x]+F[86,x]+F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[92,x]
F[100,x] = F[96,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[51,x]
F[105,x] = F[103,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[45,x]
F[111,x] = F[108,x]+F[112,x]
F[112,x] = 2*F[27,x]+F[113,x]+F[116,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[51,x]
F[115,x] = F[112,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[108,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[38,x]
F[122,x] = F[120,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[88,x]
F[125,x] = F[126,x]+F[160,x]+F[27,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[133,x]
F[128,x] = F[11,x]+F[129,x]
F[129,x] = F[130,x]+F[27,x]+F[61,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]+F[23,x]
F[132,x] = F[32,x]
F[133,x] = F[125,x]+F[134,x]
F[134,x] = F[123,x]+F[135,x]+F[149,x]+F[27,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[141,x]
F[137,x] = F[129,x]+F[138,x]
F[138,x] = 2*F[27,x]+F[139,x]+F[76,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[31,x]
F[141,x] = F[134,x]+F[142,x]
F[142,x] = 2*F[27,x]+F[143,x]+F[147,x]+F[86,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[146,x]
F[145,x] = F[138,x]
F[146,x] = F[142,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[120,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[151,x]+F[159,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[30,x]
F[154,x] = F[151,x]+F[155,x]
F[155,x] = 2*F[27,x]+F[116,x]+F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[38,x]
F[158,x] = F[155,x]
F[159,x] = F[103,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[19,x]
F[162,x] = F[109,x]
F[163,x] = F[164,x]*F[4,x]
F[164,x] = F[165,x]+F[166,x]
F[165,x] = F[151,x]
F[166,x] = F[120,x]
F[167,x] = F[168,x]*F[4,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[125,x]+F[19,x]
F[170,x] = F[152,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{18}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{56}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{32}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{42}\! \left(x \right)
F_{56}\! \left(x \right) = F_{167}\! \left(x \right)+F_{27}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{70}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{60}\! \left(x \right) = F_{27}\! \left(x \right)+F_{61}\! \left(x \right)+F_{66}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \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_{32}\! \left(x \right)
F_{70}\! \left(x \right) = F_{56}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{123}\! \left(x \right)+F_{163}\! \left(x \right)+F_{27}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{74}\! \left(x \right) = F_{60}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{63}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{31}\! \left(x \right)
F_{80}\! \left(x \right) = F_{71}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{118}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{75}\! \left(x \right)
F_{85}\! \left(x \right) = F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{106}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{91}\! \left(x \right) = F_{63}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{76}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{46}\! \left(x \right)
F_{95}\! \left(x \right) = F_{88}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{101}\! \left(x \right)+F_{86}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{92}\! \left(x \right)
F_{100}\! \left(x \right) = F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{51}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{45}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{51}\! \left(x \right)
F_{115}\! \left(x \right) = F_{112}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{38}\! \left(x \right)
F_{122}\! \left(x \right) = F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{88}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{160}\! \left(x \right)+F_{27}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{133}\! \left(x \right)
F_{128}\! \left(x \right) = F_{11}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{27}\! \left(x \right)+F_{61}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{23}\! \left(x \right)
F_{132}\! \left(x \right) = F_{32}\! \left(x \right)
F_{133}\! \left(x \right) = F_{125}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{123}\! \left(x \right)+F_{135}\! \left(x \right)+F_{149}\! \left(x \right)+F_{27}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{141}\! \left(x \right)
F_{137}\! \left(x \right) = F_{129}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{139}\! \left(x \right)+F_{76}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{31}\! \left(x \right)
F_{141}\! \left(x \right) = F_{134}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{143}\! \left(x \right)+F_{147}\! \left(x \right)+F_{86}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{146}\! \left(x \right)
F_{145}\! \left(x \right) = F_{138}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{120}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{159}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{30}\! \left(x \right)
F_{154}\! \left(x \right) = F_{151}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{116}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{38}\! \left(x \right)
F_{158}\! \left(x \right) = F_{155}\! \left(x \right)
F_{159}\! \left(x \right) = F_{103}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{19}\! \left(x \right)
F_{162}\! \left(x \right) = F_{109}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{4}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{166}\! \left(x \right)
F_{165}\! \left(x \right) = F_{151}\! \left(x \right)
F_{166}\! \left(x \right) = F_{120}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{125}\! \left(x \right)+F_{19}\! \left(x \right)
F_{170}\! \left(x \right) = F_{152}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_18(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_14(x))
Eq(F_18(x), F_19(x) + F_56(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_16(x)*F_4(x))
Eq(F_25(x), F_19(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_54(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_34(x))
Eq(F_30(x), F_23(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_4(x))
Eq(F_34(x), F_26(x) + F_35(x))
Eq(F_35(x), 2*F_27(x) + F_36(x) + F_40(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_31(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_27(x) + F_43(x) + F_53(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_4(x) + F_46(x))
Eq(F_46(x), F_32(x))
Eq(F_47(x), F_42(x) + F_48(x))
Eq(F_48(x), 2*F_27(x) + F_40(x) + F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_46(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_19(x)*F_4(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_19(x) + F_42(x))
Eq(F_56(x), F_167(x) + F_27(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_70(x))
Eq(F_59(x), F_60(x) + F_7(x))
Eq(F_60(x), F_27(x) + F_61(x) + F_66(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_4(x))
Eq(F_66(x), F_4(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_32(x))
Eq(F_70(x), F_56(x) + F_71(x))
Eq(F_71(x), F_123(x) + F_163(x) + F_27(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_80(x))
Eq(F_74(x), F_60(x) + F_75(x))
Eq(F_75(x), 2*F_27(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_63(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_31(x))
Eq(F_80(x), F_71(x) + F_81(x))
Eq(F_81(x), F_118(x) + 2*F_27(x) + F_82(x) + F_86(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_75(x))
Eq(F_85(x), F_81(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_106(x) + 2*F_27(x) + F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_95(x))
Eq(F_91(x), F_63(x) + F_92(x))
Eq(F_92(x), 2*F_27(x) + F_76(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_46(x))
Eq(F_95(x), F_88(x) + F_96(x))
Eq(F_96(x), F_101(x) + 2*F_27(x) + F_86(x) + F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_92(x))
Eq(F_100(x), F_96(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_51(x))
Eq(F_105(x), F_103(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_45(x))
Eq(F_111(x), F_108(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_116(x) + 2*F_27(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_51(x))
Eq(F_115(x), F_112(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_108(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_38(x))
Eq(F_122(x), F_120(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_88(x))
Eq(F_125(x), F_126(x) + F_160(x) + F_27(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_133(x))
Eq(F_128(x), F_11(x) + F_129(x))
Eq(F_129(x), F_130(x) + F_27(x) + F_61(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_132(x) + F_23(x))
Eq(F_132(x), F_32(x))
Eq(F_133(x), F_125(x) + F_134(x))
Eq(F_134(x), F_123(x) + F_135(x) + F_149(x) + F_27(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_141(x))
Eq(F_137(x), F_129(x) + F_138(x))
Eq(F_138(x), F_139(x) + 2*F_27(x) + F_76(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_31(x))
Eq(F_141(x), F_134(x) + F_142(x))
Eq(F_142(x), F_143(x) + F_147(x) + 2*F_27(x) + F_86(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_146(x))
Eq(F_145(x), F_138(x))
Eq(F_146(x), F_142(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_120(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_151(x) + F_159(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_30(x))
Eq(F_154(x), F_151(x) + F_155(x))
Eq(F_155(x), F_116(x) + F_156(x) + 2*F_27(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_38(x))
Eq(F_158(x), F_155(x))
Eq(F_159(x), F_103(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_19(x))
Eq(F_162(x), F_109(x))
Eq(F_163(x), F_164(x)*F_4(x))
Eq(F_164(x), F_165(x) + F_166(x))
Eq(F_165(x), F_151(x))
Eq(F_166(x), F_120(x))
Eq(F_167(x), F_168(x)*F_4(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_125(x) + F_19(x))
Eq(F_170(x), F_152(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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