0132_0321_1032_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 50, 121, 291, 700, 1686, 4065, 9807, 23668, 57130, 137913, 332939, 803772, 1940462, 4684673, 11309783, 27304212, 65918178, 159140537, 384199219, 927538940, 2239277062, 5406093025, 13051463071, 31509019124, 76069501274, 183648021625, 443365544475, 1070379110524, 2584123765470, 6238626641409, 15061377048231, 36361380737812, 87784138523794, 211929657785337, 511643454094403, 1235216565974076, 2982076586042486, 7199369738058977, 17380816062160367, 41961001862379636, 101302819786919562, 244566641436218681, 590436102659356843, 1425438846754932284, 3441313796169221326, 8308066439093374849, 20057446674355970935, 48422959787805316628, 116903366249966604098, 282229692287738524729, 681362750825443653459, 1644955193938625831548, 3971273138702695316454, 9587501471344016464353, 23146276081390728245055, 55880053634125472954356, 134906383349641674153658, 325692820333408821261561, 786292024016459316676667, 1898276868366327454614780, 4582845760749114225906110, 11063968389864555906426881, 26710782540478226038759751, 64485533470821007983946260, 155681849482120242006652146, 375849232435061491997250425, 907380314352243226001152867, 2190609861139547943999556028, 5288600036631339114000264790, 12767809934402226172000085473, 30824219905435791458000435599, 74416249745273809088000956532, 179656719395983409634002348522, 433729688537240628356005653433, 1047116096470464666346013655243, 2527961881478169961048032963772, 6103039859426804588442079582638, 14734041600331779137932192128897, 35571123060090362864306463840279, 85876287720512504866545119809300, 207323698501115372597396703458722, 500523684722743250061338526726585, 1208371067946601872720073756911731, 2917265820615946995501486040549884, 7042902709178495863723045838011334, 17003071238972938722947577716572385, 41049045187124373309618201271155935, 99101161613221685342183980258884084, 239251368413567743993986161788923930, 577603898440357173330156303836731769, 1394459165294282090654298769462387291, 3366522229028921354638753842761506172, 8127503623352124799931806454985399454, 19621529475733170954502366752732304897, 47370562574818466708936539960450009063, 114362654625370104372375446673632322836
Generating function in Maple syntax:
-(x^8+x^7-5*x^6-3*x^5+2*x^4+2*x^3+2*x^2-3*x+1)/(x^2+2*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{x^{8}+x^{7}-5 x^{6}-3 x^{5}+2 x^{4}+2 x^{3}+2 x^{2}-3 x +1}{\left(x^{2}+2 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-x**8 - x**7 + 5*x**6 + 3*x**5 - 2*x**4 - 2*x**3 - 2*x**2 + 3*x - 1)/((x - 1)**2*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+2*x-1)*(x-1)^2*F(x)+x^8+x^7-5*x^6-3*x^5+2*x^4+2*x^3+2*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{8}+x^{7}-5 x^{6}-3 x^{5}+2 x^{4}+2 x^{3}+2 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,5,n = 1,3,n = 2,1,Or(n = 3,n = 4),-1,0)+1/4*(-2^(1/2)+1)*(-1-2^(1/2))^(-n)+1/4*(1+2^(1/2))*(2^(1/2)-1)^(-n)-9/2+n
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}5 & n =0 \\ 3 & n =1 \\ 1 & n =2 \\ -1 & n =3\text{ or } n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-\sqrt{2}+1\right) \left(-1-\sqrt{2}\right)^{-n}}{4}+\frac{\left(1+\sqrt{2}\right) \left(\sqrt{2}-1\right)^{-n}}{4}-\frac{9}{2}+n
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 50
a(6) = 121
a(7) = 291
a(8) = 700
a(n+2) = a(n)+2*a(n+1)-2*n+9, n >= 9
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) = 50
a \! \left(6\right) = 121
a \! \left(7\right) = 291
a \! \left(8\right) = 700
a \! \left(n +2\right) = a \! \left(n \right)+2 a \! \left(n +1\right)-2 n +9, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19367/
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[26,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[4,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[19,x]
F[26,x] = F[27,x]+F[47,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[1,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[4,x]
F[33,x] = F[27,x]+F[34,x]
F[34,x] = F[18,x]+F[35,x]+F[45,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]+F[4,x]
F[38,x] = F[39,x]
F[39,x] = x^2
F[40,x] = F[41,x]+F[43,x]
F[41,x] = F[18,x]+F[35,x]+F[42,x]
F[42,x] = F[27,x]*F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[41,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[27,x]+F[41,x]
F[47,x] = F[18,x]+F[48,x]+F[94,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[57,x]
F[50,x] = F[11,x]+F[51,x]
F[51,x] = F[18,x]+F[52,x]+F[55,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[11,x]+F[54,x]
F[54,x] = F[18,x]+F[22,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[21,x]+F[4,x]
F[57,x] = F[58,x]+F[81,x]
F[58,x] = F[18,x]+F[48,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[27,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[11,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[20,x]*F[4,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = 2*F[18,x]+F[69,x]+F[79,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[21,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[21,x]*F[4,x]
F[74,x] = F[75,x]+F[77,x]
F[75,x] = 2*F[18,x]+F[69,x]+F[76,x]
F[76,x] = F[4,x]*F[61,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[75,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[61,x]+F[75,x]
F[81,x] = F[18,x]+F[82,x]+F[89,x]+F[92,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = F[21,x]+F[85,x]
F[85,x] = F[73,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = 2*F[18,x]+F[76,x]+F[82,x]
F[88,x] = F[78,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[61,x]+F[91,x]
F[91,x] = 2*F[18,x]+F[69,x]+F[76,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[41,x]+F[75,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[60,x]+F[96,x]
F[96,x] = F[105,x]+F[97,x]
F[97,x] = F[18,x]+F[35,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[27,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[4,x]
F[104,x] = F[100,x]
F[105,x] = 2*F[18,x]+F[106,x]+F[69,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[61,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[21,x]
F[112,x] = F[108,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_{26}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{47}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
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_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{45}\! \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_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = x^{2}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{27}\! \left(x \right)+F_{41}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{94}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right)+F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{81}\! \left(x \right)
F_{58}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{27}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{61}\! \left(x \right)+F_{75}\! \left(x \right)
F_{81}\! \left(x \right) = F_{18}\! \left(x \right)+F_{82}\! \left(x \right)+F_{89}\! \left(x \right)+F_{92}\! \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_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{21}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{73}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{88}\! \left(x \right) = F_{78}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{61}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{41}\! \left(x \right)+F_{75}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{60}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{105}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{27}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \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_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{100}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{106}\! \left(x \right)+F_{69}\! \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_{61}\! \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_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{21}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \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_26(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_4(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_19(x))
Eq(F_26(x), F_27(x) + F_47(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_1(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_4(x))
Eq(F_33(x), F_27(x) + F_34(x))
Eq(F_34(x), F_18(x) + F_35(x) + F_45(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x) + F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), x**2)
Eq(F_40(x), F_41(x) + F_43(x))
Eq(F_41(x), F_18(x) + F_35(x) + F_42(x))
Eq(F_42(x), F_27(x)*F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_41(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_27(x) + F_41(x))
Eq(F_47(x), F_18(x) + F_48(x) + F_94(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_57(x))
Eq(F_50(x), F_11(x) + F_51(x))
Eq(F_51(x), F_18(x) + F_52(x) + F_55(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_11(x) + F_54(x))
Eq(F_54(x), F_18(x) + F_22(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_21(x) + F_4(x))
Eq(F_57(x), F_58(x) + F_81(x))
Eq(F_58(x), F_18(x) + F_48(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_27(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_11(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_20(x)*F_4(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), 2*F_18(x) + F_69(x) + F_79(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_21(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_21(x)*F_4(x))
Eq(F_74(x), F_75(x) + F_77(x))
Eq(F_75(x), 2*F_18(x) + F_69(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_61(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_75(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_61(x) + F_75(x))
Eq(F_81(x), F_18(x) + F_82(x) + F_89(x) + F_92(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), F_21(x) + F_85(x))
Eq(F_85(x), F_73(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), 2*F_18(x) + F_76(x) + F_82(x))
Eq(F_88(x), F_78(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_61(x) + F_91(x))
Eq(F_91(x), 2*F_18(x) + F_69(x) + F_76(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_41(x) + F_75(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_60(x) + F_96(x))
Eq(F_96(x), F_105(x) + F_97(x))
Eq(F_97(x), F_18(x) + F_35(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_27(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_4(x))
Eq(F_104(x), F_100(x))
Eq(F_105(x), F_106(x) + 2*F_18(x) + F_69(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_61(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_112(x))
Eq(F_111(x), F_21(x))
Eq(F_112(x), F_108(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": [0, 3, 2, 1], "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": [0, 3, 2, 1], "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": [0, 3, 2, 1], "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, 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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"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, 0], [0, 1], [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, 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": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"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, 0], [1, 2], [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": [2, 1, 0], "pos": [[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, 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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"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, 0], [0, 1], [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, 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": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"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, 0], [0, 1], [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": [2, 1, 0], "pos": [[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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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