0321_1032_1230_3012

Counting sequence:
1, 1, 2, 6, 20, 56, 133, 309, 724, 1716, 4101, 9849, 23716, 57184, 137973, 333005, 803844, 1940540, 4684757, 11309873, 27304308, 65918280, 159140645, 384199333, 927539060, 2239277188, 5406093157, 13051463209, 31509019268, 76069501424, 183648021781, 443365544637, 1070379110692, 2584123765644, 6238626641589, 15061377048417, 36361380738004, 87784138523992, 211929657785541, 511643454094613, 1235216565974292, 2982076586042708, 7199369738059205, 17380816062160601, 41961001862379876, 101302819786919808, 244566641436218933, 590436102659357101, 1425438846754932548, 3441313796169221596, 8308066439093375125, 20057446674355971217, 48422959787805316916, 116903366249966604392, 282229692287738525029, 681362750825443653765, 1644955193938625831860, 3971273138702695316772, 9587501471344016464677, 23146276081390728245385, 55880053634125472954692, 134906383349641674154000, 325692820333408821261909, 786292024016459316677021, 1898276868366327454615140, 4582845760749114225906476, 11063968389864555906427253, 26710782540478226038760129, 64485533470821007983946644, 155681849482120242006652536, 375849232435061491997250821, 907380314352243226001153269, 2190609861139547943999556436, 5288600036631339114000265204, 12767809934402226172000085893, 30824219905435791458000436025, 74416249745273809088000956964, 179656719395983409634002348960, 433729688537240628356005653877, 1047116096470464666346013655693, 2527961881478169961048032964228, 6103039859426804588442079583100, 14734041600331779137932192129365, 35571123060090362864306463840753, 85876287720512504866545119809780, 207323698501115372597396703459208, 500523684722743250061338526727077, 1208371067946601872720073756912229, 2917265820615946995501486040550388, 7042902709178495863723045838011844, 17003071238972938722947577716572901, 41049045187124373309618201271156457, 99101161613221685342183980258884612, 239251368413567743993986161788924464, 577603898440357173330156303836732309, 1394459165294282090654298769462387837, 3366522229028921354638753842761506724, 8127503623352124799931806454985400012, 19621529475733170954502366752732305461, 47370562574818466708936539960450009633, 114362654625370104372375446673632323412

Generating function in Maple syntax:
(x+1)*(5*x^6+8*x^5-7*x^4+4*x^3-6*x^2+4*x-1)/(x^2+2*x-1)/(x-1)^2

Generating function in latex syntax:
\frac{\left(x +1\right) \left(5 x^{6}+8 x^{5}-7 x^{4}+4 x^{3}-6 x^{2}+4 x -1\right)}{\left(x^{2}+2 x -1\right) \left(x -1\right)^{2}}

Generating function in sympy syntax:
(x + 1)*(5*x**6 + 8*x**5 - 7*x**4 + 4*x**3 - 6*x**2 + 4*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+1)*(5*x^6+8*x^5-7*x^4+4*x^3-6*x^2+4*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)+\left(x +1\right) \left(5 x^{6}+8 x^{5}-7 x^{4}+4 x^{3}-6 x^{2}+4 x -1\right) = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,29,n = 1,21,n = 2,13,n = 3,5,0)+1/4*(-2^(1/2)+1)*(-1-2^(1/2))^(-n)+1/4*(1+2^(1/2))*(2^(1/2)-1)^(-n)-57/2+7*n

Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}29 & n =0 \\ 21 & n =1 \\ 13 & n =2 \\ 5 & n =3 \\ 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{57}{2}+7 n

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 56
a(6) = 133
a(7) = 309
a(n+2) = a(n)+2*a(n+1)+57-14*n, n >= 8

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 56
a \! \left(6\right) = 133
a \! \left(7\right) = 309
a \! \left(n +2\right) = a \! \left(n \right)+2 a \! \left(n +1\right)+57-14 n, \quad n \geq 8

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15937/
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[39,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[6,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[26,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[15,x]+F[22,x]+F[23,x]
F[22,x] = F[18,x]*F[4,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[4,x]
F[25,x] = F[22,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[32,x]
F[28,x] = F[11,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[18,x]+F[25,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[25,x]
F[39,x] = F[40,x]+F[60,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]*F[4,x]
F[46,x] = F[40,x]+F[47,x]
F[47,x] = F[15,x]+F[48,x]+F[58,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[4,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = x^2
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[15,x]+F[48,x]+F[55,x]
F[55,x] = F[4,x]*F[40,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[54,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[40,x]+F[54,x]
F[60,x] = F[103,x]+F[15,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[66,x]
F[63,x] = F[18,x]+F[64,x]
F[64,x] = F[15,x]+F[23,x]+F[65,x]
F[65,x] = F[17,x]*F[4,x]
F[66,x] = F[67,x]+F[90,x]
F[67,x] = F[15,x]+F[61,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[40,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[18,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[31,x]*F[4,x]
F[76,x] = F[70,x]+F[77,x]
F[77,x] = 2*F[15,x]+F[78,x]+F[88,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[25,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[25,x]*F[4,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = 2*F[15,x]+F[78,x]+F[85,x]
F[85,x] = F[4,x]*F[70,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[84,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[70,x]+F[84,x]
F[90,x] = F[101,x]+F[15,x]+F[91,x]+F[98,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[95,x]
F[93,x] = F[25,x]+F[94,x]
F[94,x] = F[82,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = 2*F[15,x]+F[85,x]+F[91,x]
F[97,x] = F[87,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[70,x]
F[100,x] = 2*F[15,x]+F[78,x]+F[85,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[54,x]+F[84,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[107,x]
F[105,x] = F[106,x]+F[40,x]
F[106,x] = F[71,x]
F[107,x] = F[108,x]+F[116,x]
F[108,x] = F[109,x]+F[15,x]+F[48,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[40,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[4,x]
F[115,x] = F[111,x]
F[116,x] = 2*F[15,x]+F[117,x]+F[78,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[70,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[25,x]
F[123,x] = F[120,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_{39}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \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_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \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_{25}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{60}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{58}\! \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_{53}\! \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_{52}\! \left(x \right) = x^{2}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{40}\! \left(x \right)+F_{54}\! \left(x \right)
F_{60}\! \left(x \right) = F_{103}\! \left(x \right)+F_{15}\! \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_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{18}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{90}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right)+F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{40}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \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_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x \right)+F_{88}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{25}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{70}\! \left(x \right)+F_{84}\! \left(x \right)
F_{90}\! \left(x \right) = F_{101}\! \left(x \right)+F_{15}\! \left(x \right)+F_{91}\! \left(x \right)+F_{98}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{25}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{82}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{97}\! \left(x \right) = F_{87}\! \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_{70}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{54}\! \left(x \right)+F_{84}\! \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_{107}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{40}\! \left(x \right)
F_{106}\! \left(x \right) = F_{71}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{116}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{15}\! \left(x \right)+F_{48}\! \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_{40}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{111}\! \left(x \right)
F_{116}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{117}\! \left(x \right)+F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{70}\! \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_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{25}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \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_39(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_6(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_26(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_15(x) + F_22(x) + F_23(x))
Eq(F_22(x), F_18(x)*F_4(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_4(x))
Eq(F_25(x), F_22(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_32(x))
Eq(F_28(x), F_11(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_18(x) + F_25(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(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_25(x))
Eq(F_39(x), F_40(x) + F_60(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)*F_4(x))
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), F_15(x) + F_48(x) + F_58(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_4(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), x**2)
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_15(x) + F_48(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_40(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_54(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_40(x) + F_54(x))
Eq(F_60(x), F_103(x) + F_15(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_66(x))
Eq(F_63(x), F_18(x) + F_64(x))
Eq(F_64(x), F_15(x) + F_23(x) + F_65(x))
Eq(F_65(x), F_17(x)*F_4(x))
Eq(F_66(x), F_67(x) + F_90(x))
Eq(F_67(x), F_15(x) + F_61(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_40(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_18(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_31(x)*F_4(x))
Eq(F_76(x), F_70(x) + F_77(x))
Eq(F_77(x), 2*F_15(x) + F_78(x) + F_88(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_25(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_25(x)*F_4(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), 2*F_15(x) + F_78(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_70(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_84(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_70(x) + F_84(x))
Eq(F_90(x), F_101(x) + F_15(x) + F_91(x) + F_98(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_95(x))
Eq(F_93(x), F_25(x) + F_94(x))
Eq(F_94(x), F_82(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), 2*F_15(x) + F_85(x) + F_91(x))
Eq(F_97(x), F_87(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_70(x))
Eq(F_100(x), 2*F_15(x) + F_78(x) + F_85(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_54(x) + F_84(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_107(x))
Eq(F_105(x), F_106(x) + F_40(x))
Eq(F_106(x), F_71(x))
Eq(F_107(x), F_108(x) + F_116(x))
Eq(F_108(x), F_109(x) + F_15(x) + F_48(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_40(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_4(x))
Eq(F_115(x), F_111(x))
Eq(F_116(x), F_117(x) + 2*F_15(x) + F_78(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_70(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_123(x))
Eq(F_122(x), F_25(x))
Eq(F_123(x), F_120(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, 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, 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, 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": [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, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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": [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, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"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": [2, 1, 0], "pos": [[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": []}, {"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": [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, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 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