0132_1023_1032_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 52, 129, 314, 768, 1901, 4766, 12078, 30863, 79352, 204950, 531119, 1379800, 3591280, 9360341, 24422782, 63774724, 166635785, 435602874, 1139115562, 2979632755, 7795566092, 20398641034, 53383521979, 139718277188, 365704050076, 957259411881, 2505805356578, 6559619150568, 17171977324037, 44954163672950, 117686216034054, 308095890137015, 806584267457600, 2111622541090526, 5528214617881127, 14472883843737424, 37890161987107240, 99197052283592669, 259699895225549542, 679900434165130540, 1779997008892169057, 4660081795882524114, 12200230785702368194, 31940575375449672283, 83621424969632662676, 218923558792287334546, 573148969926310198003, 1500522788027074781948, 3928418268239449818772, 10284729764866288448625, 26925766522719058131914, 70492560796025728643280, 184551897850852985730845, 483163096727563674439886, 1264937320273964831933022, 3311648719978691042632799, 8670008551431001273658120, 22698376357852377901455014, 59425119369202714379804447, 155576979443909660006749000, 407305814350835237751487072, 1066340454385215910913856869, 2791715530358055306339888334, 7308806099795440640266985428, 19134702695241255984262502201, 50095301838354319167064033386, 131151202524673706446436341978, 343358305145370844366618840003, 898923711730846970597947947932, 2353412827685986445207420973850, 6161314766604745266031627414699, 16130531462683515390240147079220, 42230279602556333360179166864140, 110560307307206550217401101940921, 289450642243505449343139659577842, 757791619272194063527279984135224, 1983924215270845275279163597375925, 5193981025935878834614107573050534, 13598018861327865380003861897710902, 35600075555629865619334763073728135, 93202207800726028123763785878354512, 244006547836876812072427979720456174, 638817435690561594781296380298197399, 1672445759196122345722791739950797248, 4378519841820434189412351578550746776, 11463113766110437716763198179884065901, 30010821456201393949696114617099437878, 78569350601874774110482279977232474108, 205697230348184988338905386207689424017, 538522340440204310821902983707295909250, 1409869790967476183960341950593850738034, 3691087032452320720729759598265570609835, 9663391306369678937575970438974231341860, 25299086886617102010701539001420614985506, 66233869353402398931950501358424089455587, 173402521173431638460018074980954848825324
Generating function in Maple syntax:
-(2*x^12-9*x^11+10*x^10+9*x^9-29*x^8+11*x^7+2*x^6+x^5+19*x^4-36*x^3+25*x^2-8*x+1)/(2*x-1)/(x^2-3*x+1)/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{2 x^{12}-9 x^{11}+10 x^{10}+9 x^{9}-29 x^{8}+11 x^{7}+2 x^{6}+x^{5}+19 x^{4}-36 x^{3}+25 x^{2}-8 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-2*x**12 + 9*x**11 - 10*x**10 - 9*x**9 + 29*x**8 - 11*x**7 - 2*x**6 - x**5 - 19*x**4 + 36*x**3 - 25*x**2 + 8*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x^2+x-1)*(x-1)^3*F(x)+2*x^12-9*x^11+10*x^10+9*x^9-29*x^8+11*x^7+2*x^6+x^5+19*x^4-36*x^3+25*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{12}-9 x^{11}+10 x^{10}+9 x^{9}-29 x^{8}+11 x^{7}+2 x^{6}+x^{5}+19 x^{4}-36 x^{3}+25 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
-piecewise(n = 0,21/2,n = 1,4,n = 2,2,Or(n = 3,n = 4),1,0)+1/10*(5-5^(1/2))*(3/2-1/2*5^(1/2))^(-n)+1/10*(5+5^(1/2))*(3/2+1/2*5^(1/2))^(-n)+1/10*(5+5^(1/2))*(-1/2*5^(1/2)-1/2)^(-n)+1/10*(5-5^(1/2))*(1/2*5^(1/2)-1/2)^(-n)+n^2-7*n+2^(-1+n)+9
Explicit closed form in latex syntax:
-\left(\left\{\begin{array}{cc}\frac{21}{2} & n =0 \\ 4 & n =1 \\ 2 & n =2 \\ 1 & n =3\text{ or } n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(5-\sqrt{5}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(5+\sqrt{5}\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(5+\sqrt{5}\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+\frac{\left(5-\sqrt{5}\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+n^{2}-7 n +2^{-1+n}+9
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(6) = 129
a(7) = 314
a(8) = 768
a(9) = 1901
a(10) = 4766
a(11) = 12078
a(12) = 30863
a(n+5) = -n^2+4*a(n+2)-11*a(n+3)+6*a(n+4)-2*a(n)+5*a(n+1)+9*n-9, n >= 13
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) = 52
a \! \left(6\right) = 129
a \! \left(7\right) = 314
a \! \left(8\right) = 768
a \! \left(9\right) = 1901
a \! \left(10\right) = 4766
a \! \left(11\right) = 12078
a \! \left(12\right) = 30863
a \! \left(n +5\right) = -n^{2}+4 a \! \left(n +2\right)-11 a \! \left(n +3\right)+6 a \! \left(n +4\right)-2 a \! \left(n \right)+5 a \! \left(n +1\right)+9 n -9, \quad n \geq 13
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19577/
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[44,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[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[19,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]+F[41,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]+F[4,x]
F[30,x] = F[31,x]
F[31,x] = x^2
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[20,x]+F[25,x]+F[27,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[29,x]+F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[35,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[14,x]+F[43,x]
F[43,x] = F[37,x]
F[44,x] = F[45,x]+F[64,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[48,x]
F[51,x] = F[45,x]+F[52,x]
F[52,x] = F[20,x]+F[53,x]+F[63,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[49,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[20,x]+F[53,x]+F[60,x]
F[60,x] = F[4,x]*F[45,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[52,x]
F[63,x] = F[4,x]*F[51,x]
F[64,x] = F[20,x]+F[65,x]+F[86,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[4,x]+F[68,x]
F[68,x] = F[20,x]+F[57,x]+F[69,x]
F[69,x] = F[4,x]*F[67,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[20,x]+F[60,x]+F[65,x]
F[72,x] = F[20,x]+F[62,x]+F[73,x]+F[74,x]
F[73,x] = 0
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[85,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[4,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[79,x]
F[82,x] = F[76,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[82,x]
F[85,x] = F[74,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[45,x]+F[89,x]
F[89,x] = F[77,x]
F[90,x] = F[106,x]+F[91,x]
F[91,x] = F[20,x]+F[53,x]+F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[100,x]+F[94,x]
F[94,x] = F[45,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[4,x]
F[99,x] = F[95,x]
F[100,x] = F[101,x]+F[91,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[95,x]
F[105,x] = F[101,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[76,x]
F[110,x] = F[107,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_{44}\! \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_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{41}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = x^{2}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{64}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{20}\! \left(x \right)+F_{53}\! \left(x \right)+F_{63}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right)+F_{65}\! \left(x \right)+F_{86}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{57}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)+F_{60}\! \left(x \right)+F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{20}\! \left(x \right)+F_{62}\! \left(x \right)+F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = 0
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{85}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{74}\! \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_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{45}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{77}\! \left(x \right)
F_{90}\! \left(x \right) = F_{106}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{20}\! \left(x \right)+F_{53}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{100}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{45}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right)
F_{99}\! \left(x \right) = F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{91}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{95}\! \left(x \right)
F_{105}\! \left(x \right) = F_{101}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{76}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \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_44(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) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_41(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x) + F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), x**2)
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_20(x) + F_25(x) + F_27(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_29(x) + F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_35(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_43(x))
Eq(F_43(x), F_37(x))
Eq(F_44(x), F_45(x) + F_64(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_48(x))
Eq(F_51(x), F_45(x) + F_52(x))
Eq(F_52(x), F_20(x) + F_53(x) + F_63(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_49(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_20(x) + F_53(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_45(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_52(x))
Eq(F_63(x), F_4(x)*F_51(x))
Eq(F_64(x), F_20(x) + F_65(x) + F_86(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_4(x) + F_68(x))
Eq(F_68(x), F_20(x) + F_57(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_67(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_20(x) + F_60(x) + F_65(x))
Eq(F_72(x), F_20(x) + F_62(x) + F_73(x) + F_74(x))
Eq(F_73(x), 0)
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_85(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_4(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_79(x))
Eq(F_82(x), F_76(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_82(x))
Eq(F_85(x), F_74(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_45(x) + F_89(x))
Eq(F_89(x), F_77(x))
Eq(F_90(x), F_106(x) + F_91(x))
Eq(F_91(x), F_20(x) + F_53(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_100(x) + F_94(x))
Eq(F_94(x), F_45(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_4(x))
Eq(F_99(x), F_95(x))
Eq(F_100(x), F_101(x) + F_91(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_95(x))
Eq(F_105(x), F_101(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_76(x))
Eq(F_110(x), F_107(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], 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