0123_0231_1032
Counting sequence:
1, 1, 2, 6, 21, 74, 259, 905, 3163, 11058, 38664, 135193, 472724, 1652965, 5779907, 20210571, 70670238, 247112450, 864077593, 3021418466, 10564988371, 36942575637, 129177037563, 451693114846, 1579434503132, 5522805791005, 19311585094940, 67526784937389, 236120787686511, 825643134498227, 2887024866494482, 10095054668915438, 35299359541791325, 123431207153135562, 431601680513369811, 1509180821596187857, 5277149870141113979, 18452600479296403498, 64523174976538378688, 225618070131855108033, 788918300882311658196, 2758609206715123555013, 9646023861865855547467, 33729234324742158671291, 117940953124835406367942, 412403919106780898530602, 1442052043742711926988001, 5042420793106231700717698, 17631823736929245468741827, 61653166414664207853325885, 215582516344748784562302491, 753826997967124703403035862, 2635905510794772479037853428, 9216966068574345366441144965, 32228948709028702121608594876, 112694907105138867196527512045, 394060079405507498223289419607, 1377909172383478387806646659171, 4818132529950422842666009568250, 16847555369713286805346438886902, 58910816622654345060119190324773, 205993346749099807534671813670282, 720296565853018939424173700158307, 2518659709003051711983339207952089, 8806992883886382825805694107704603, 30795396209965499347696309405498274, 107682206654658174652468579319174584, 376532178737293793674469962592099561, 1316619393576666803695709411260342996, 4603820670401830666236518855299540965, 16098171475084660601226664953985670547, 56290447303328652337321787166593761387, 196830706053350456191783240558374689006, 688257576577642184186253693682389629842, 2406629032708617315638895940635617370281, 8415255419164479364161347029666415448930, 29425608520177463545849377111914709533043, 102892472498322495373326494036148685073189, 359783923909628718250512355490285575134907, 1258055800981164114852481704432644639006030, 4399041461285261392535795254080405835078732, 15382120382112131574598777998991319417327469, 53786632731726876290369206116996111768613404, 188075622134770506495040909182065230980762733, 657643690353495538377430008780034407845461247, 2299581511695591019134057794734488634532588179, 8040942544571122245946508029997155952647866338, 28116749363417610084621118880195609482714828350, 98315787034069652821011925068695201496573889005, 343780636061181942132221583821055953705280666506, 1202097133084799473540002364972460367303213209779, 4203370887688751912836199617900621088599497614753, 14697919438614076135983118246821385268622870823483, 51394188520626653268031648633489399128050547400602, 179709966755864651433741378187116905141634331038960, 628391518205066400226603399904108023504457811779473, 2197295493847070810456817604080481235546732672559764, 7683279209546969710079814034687793704493866895532613, 26866108621786178341758355649629973226922724956897691, 93942673797503774932877124353322007638006576696447387, 328489178855909131986811889869870558730147357022364182
Generating function in Maple syntax:
(2*x^4-4*x^3+7*x^2-5*x+1)/(4*x^4-9*x^3+11*x^2-6*x+1)
Generating function in latex syntax:
\frac{2 x^{4}-4 x^{3}+7 x^{2}-5 x +1}{4 x^{4}-9 x^{3}+11 x^{2}-6 x +1}
Generating function in sympy syntax:
(2*x**4 - 4*x**3 + 7*x**2 - 5*x + 1)/(4*x**4 - 9*x**3 + 11*x**2 - 6*x + 1)
Implicit equation for the generating function in Maple syntax:
(4*x^4-9*x^3+11*x^2-6*x+1)*F(x)-2*x^4+4*x^3-7*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{4}-9 x^{3}+11 x^{2}-6 x +1\right) F \! \left(x \right)-2 x^{4}+4 x^{3}-7 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
-188/597*Sum(_alpha^(-n+2),_alpha = RootOf(4*_Z^4-9*_Z^3+11*_Z^2-6*_Z+1))+147/199*Sum(_alpha^(-n+1),_alpha = RootOf(4*_Z^4-9*_Z^3+11*_Z^2-6*_Z+1))-320/597*Sum(_alpha^(-n),_alpha = RootOf(4*_Z^4-9*_Z^3+11*_Z^2-6*_Z+1))+28/199*Sum(_alpha^(-n-1),_alpha = RootOf(4*_Z^4-9*_Z^3+11*_Z^2-6*_Z+1))+piecewise(n = 0,1/2,0)
Explicit closed form in latex syntax:
-\frac{188 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-9 \textit{\_Z}^{3}+11 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{597}+\frac{147 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-9 \textit{\_Z}^{3}+11 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{199}-\frac{320 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-9 \textit{\_Z}^{3}+11 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{597}+\frac{28 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(4 \textit{\_Z}^{4}-9 \textit{\_Z}^{3}+11 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{199}+\left(\left\{\begin{array}{cc}\frac{1}{2} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(n+4) = -4*a(n)+9*a(n+1)-11*a(n+2)+6*a(n+3), n >= 5
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) = 21
a \! \left(n +4\right) = -4 a \! \left(n \right)+9 a \! \left(n +1\right)-11 a \! \left(n +2\right)+6 a \! \left(n +3\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14638/
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[20,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[7,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[4,x]
F[18,x] = F[19,x]
F[19,x] = F[15,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[93,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[38,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[1,x]+F[4,x]
F[29,x] = F[22,x]+F[30,x]+F[36,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]+F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[4,x]
F[35,x] = F[19,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[19,x]+F[7,x]
F[38,x] = F[39,x]+F[82,x]
F[39,x] = F[22,x]+F[23,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[2,x]+F[42,x]
F[42,x] = F[22,x]+F[43,x]+F[81,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[4,x]+F[46,x]
F[46,x] = F[22,x]+F[30,x]+F[47,x]
F[47,x] = F[4,x]*F[7,x]
F[48,x] = F[42,x]+F[49,x]
F[49,x] = F[22,x]+F[50,x]+F[71,x]+F[80,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[59,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[4,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[19,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = 2*F[22,x]+F[50,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[42,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = 2*F[22,x]+F[50,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[42,x]
F[70,x] = F[66,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[79,x]
F[73,x] = F[42,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[22,x]+F[43,x]+F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[2,x]+F[76,x]
F[79,x] = F[66,x]
F[80,x] = F[21,x]*F[4,x]
F[81,x] = F[2,x]*F[4,x]
F[82,x] = F[22,x]+F[71,x]+F[83,x]+F[91,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[54,x]
F[87,x] = F[57,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = 2*F[22,x]+F[61,x]+F[83,x]
F[90,x] = F[64,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[21,x]+F[66,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[78,x]+F[95,x]
F[95,x] = F[21,x]+F[96,x]
F[96,x] = 2*F[22,x]+F[50,x]+F[67,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_{20}\! \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_{7}\! \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_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{93}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{82}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)+F_{81}\! \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_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)+F_{71}\! \left(x \right)+F_{80}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)
F_{56}\! \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_{19}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{50}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{42}\! \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_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{50}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{42}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{79}\! \left(x \right)
F_{73}\! \left(x \right) = F_{42}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \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_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{66}\! \left(x \right)
F_{80}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{22}\! \left(x \right)+F_{71}\! \left(x \right)+F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{54}\! \left(x \right)
F_{87}\! \left(x \right) = F_{57}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{61}\! \left(x \right)+F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{64}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{21}\! \left(x \right)+F_{66}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{78}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{21}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{50}\! \left(x \right)+F_{67}\! \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_20(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_7(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_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_93(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_38(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_1(x) + F_4(x))
Eq(F_29(x), F_22(x) + F_30(x) + F_36(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x) + F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_4(x))
Eq(F_35(x), F_19(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_19(x) + F_7(x))
Eq(F_38(x), F_39(x) + F_82(x))
Eq(F_39(x), F_22(x) + F_23(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_2(x) + F_42(x))
Eq(F_42(x), F_22(x) + F_43(x) + F_81(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_4(x) + F_46(x))
Eq(F_46(x), F_22(x) + F_30(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_7(x))
Eq(F_48(x), F_42(x) + F_49(x))
Eq(F_49(x), F_22(x) + F_50(x) + F_71(x) + F_80(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_59(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_4(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_19(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), 2*F_22(x) + F_50(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_42(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), 2*F_22(x) + F_50(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_42(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_79(x))
Eq(F_73(x), F_42(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_22(x) + F_43(x) + F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_2(x) + F_76(x))
Eq(F_79(x), F_66(x))
Eq(F_80(x), F_21(x)*F_4(x))
Eq(F_81(x), F_2(x)*F_4(x))
Eq(F_82(x), F_22(x) + F_71(x) + F_83(x) + F_91(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_54(x))
Eq(F_87(x), F_57(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), 2*F_22(x) + F_61(x) + F_83(x))
Eq(F_90(x), F_64(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_21(x) + F_66(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_78(x) + F_95(x))
Eq(F_95(x), F_21(x) + F_96(x))
Eq(F_96(x), 2*F_22(x) + F_50(x) + F_67(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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{"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [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, 0, 3, 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", 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