0132_0231_1230_3120
Counting sequence:
1, 1, 2, 6, 20, 67, 219, 691, 2099, 6147, 17411, 47875, 128259, 335875, 862211, 2174979, 5402627, 13238275, 32047107, 76742659, 181993475, 427819011, 997720067, 2310012931, 5313134595, 12146704387, 27615297539, 62461575171, 140609847299, 315143225347, 703435112451, 1564173402115, 3465770172419, 7653631721475, 16849156702211, 36983963385859, 80955838562307, 176746494164995, 384932148936707, 836384751353859, 1813300832632835, 3923057487904771, 8470637580386307, 18255191555964931, 39271256809275395, 84336939896930307, 180821284257529859, 387080869535285251, 827378101854928899, 1765974003882655747, 3764164863551602691, 8012748162022244355, 17035147065505611779, 36172912207039823875, 76721071452070084611, 162539414151428571139, 343980435938931113987, 727205239030768730115, 1535835559324396027907, 3240502061479657209859, 6830843742013454548995, 14386154534484236566531, 30271683485709677625347, 63644725818811773616131, 133700848124742223265795, 280648764337417118285827, 588654050136145501618179, 1233773583881915940732931, 2584038356589307699920899, 5408290214506461180985347, 11311691039951286727344131, 23643413240202416820846595, 49387394121566287703310339, 103098705054010094305411075, 215094348561746600193425411, 448487867244613075589922819, 934598828258248614597361667, 1946521685307004799923781635, 4051903779097744464836296707, 8430066413763986978196422659, 17529953289458204433503485955, 36434606351545694067294732291, 75689636640252317999178973187, 157163983327360636599326998531, 326188737870960400031696289795, 676688973974370992766733778947, 1403195363123421624564759658499, 2908443408235431785541515870211, 6025885912165840662806235447299, 12479673536035918551258071302147, 25835189649866243647007272992771, 53462606991607896586999753080835, 110591682894569268203181987332099, 228682187577109727421565419651075, 472697500480808174928031391940611, 976739642756322178416508609232899, 2017540206665584215298497098809347, 4165975241325047399343727996567555, 8599345531135736938065666825519107, 17744810786482297955163632100704259, 36604757960352866461956395302387715
Generating function in Maple syntax:
(x^5-22*x^4+36*x^3-25*x^2+8*x-1)/(-1+x)/(2*x-1)^4
Generating function in latex syntax:
\frac{x^{5}-22 x^{4}+36 x^{3}-25 x^{2}+8 x -1}{\left(-1+x \right) \left(2 x -1\right)^{4}}
Generating function in sympy syntax:
(x**5 - 22*x**4 + 36*x**3 - 25*x**2 + 8*x - 1)/((x - 1)*(2*x - 1)**4)
Implicit equation for the generating function in Maple syntax:
(-1+x)*(2*x-1)^4*F(x)-x^5+22*x^4-36*x^3+25*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+x \right) \left(2 x -1\right)^{4} F \! \left(x \right)-x^{5}+22 x^{4}-36 x^{3}+25 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,3+1/32*(n^3-8*n^2+41*n-66)*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 3+\frac{\left(n^{3}-8 n^{2}+41 n -66\right) 2^{n}}{32} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 67
a(n+4) = -16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3)+3, n >= 6
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) = 67
a \! \left(n +4\right) = -16 a \! \left(n \right)+32 a \! \left(n +1\right)-24 a \! \left(n +2\right)+8 a \! \left(n +3\right)+3, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15356/
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[12,x]*F[4,x]
F[4,x] = F[22,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[17,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[32,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[23,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[14,x]
F[31,x] = F[27,x]
F[32,x] = F[18,x]+F[33,x]+F[90,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[47,x]
F[35,x] = F[36,x]+F[6,x]
F[36,x] = F[18,x]+F[19,x]+F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[13,x]+F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[14,x]+F[40,x]
F[43,x] = 2*F[18,x]+F[44,x]+F[46,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[17,x]+F[43,x]
F[46,x] = F[12,x]*F[39,x]
F[47,x] = F[32,x]+F[48,x]
F[48,x] = 2*F[18,x]+F[49,x]+F[53,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[36,x]
F[52,x] = F[48,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[62,x]
F[55,x] = F[27,x]+F[56,x]
F[56,x] = 2*F[18,x]+F[57,x]+F[61,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[17,x]
F[60,x] = F[56,x]
F[61,x] = F[12,x]*F[55,x]
F[62,x] = F[63,x]+F[75,x]
F[63,x] = 2*F[18,x]+F[64,x]+F[73,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[40,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[40,x]
F[72,x] = F[68,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[27,x]+F[63,x]
F[75,x] = 2*F[18,x]+F[76,x]+F[87,x]+F[89,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[43,x]
F[79,x] = F[80,x]
F[80,x] = 3*F[18,x]+F[81,x]+F[85,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[43,x]
F[84,x] = F[80,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[68,x]+F[80,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[56,x]+F[75,x]
F[89,x] = F[12,x]*F[62,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[92,x]+F[98,x]
F[92,x] = F[23,x]+F[93,x]
F[93,x] = F[18,x]+F[94,x]+F[97,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[20,x]+F[96,x]
F[96,x] = F[56,x]+F[93,x]
F[97,x] = F[12,x]*F[92,x]
F[98,x] = F[106,x]+F[99,x]
F[99,x] = F[100,x]+F[104,x]+F[18,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[14,x]+F[40,x]
F[103,x] = F[27,x]+F[68,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[23,x]+F[99,x]
F[106,x] = F[107,x]+F[111,x]+F[113,x]+F[18,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[17,x]+F[43,x]
F[110,x] = F[56,x]+F[80,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[106,x]+F[93,x]
F[113,x] = F[12,x]*F[98,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
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_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{90}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{17}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{36}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{55}\! \left(x \right) = F_{27}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{17}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{75}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{64}\! \left(x \right)+F_{73}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{40}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{40}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{27}\! \left(x \right)+F_{63}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{76}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{43}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{43}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{68}\! \left(x \right)+F_{80}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{56}\! \left(x \right)+F_{75}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{92}\! \left(x \right) = F_{23}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{18}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{20}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{56}\! \left(x \right)+F_{93}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{98}\! \left(x \right) = F_{106}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{104}\! \left(x \right)+F_{18}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{103}\! \left(x \right) = F_{27}\! \left(x \right)+F_{68}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{23}\! \left(x \right)+F_{99}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)+F_{113}\! \left(x \right)+F_{18}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{17}\! \left(x \right)+F_{43}\! \left(x \right)
F_{110}\! \left(x \right) = F_{56}\! \left(x \right)+F_{80}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{106}\! \left(x \right)+F_{93}\! \left(x \right)
F_{113}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_22(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_17(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_32(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_23(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_14(x))
Eq(F_31(x), F_27(x))
Eq(F_32(x), F_18(x) + F_33(x) + F_90(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_47(x))
Eq(F_35(x), F_36(x) + F_6(x))
Eq(F_36(x), F_18(x) + F_19(x) + F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_13(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_14(x) + F_40(x))
Eq(F_43(x), 2*F_18(x) + F_44(x) + F_46(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_17(x) + F_43(x))
Eq(F_46(x), F_12(x)*F_39(x))
Eq(F_47(x), F_32(x) + F_48(x))
Eq(F_48(x), 2*F_18(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_36(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_62(x))
Eq(F_55(x), F_27(x) + F_56(x))
Eq(F_56(x), 2*F_18(x) + F_57(x) + F_61(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_17(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_12(x)*F_55(x))
Eq(F_62(x), F_63(x) + F_75(x))
Eq(F_63(x), 2*F_18(x) + F_64(x) + F_73(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_40(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_40(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_27(x) + F_63(x))
Eq(F_75(x), 2*F_18(x) + F_76(x) + F_87(x) + F_89(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_43(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), 3*F_18(x) + F_81(x) + F_85(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_43(x))
Eq(F_84(x), F_80(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_68(x) + F_80(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_56(x) + F_75(x))
Eq(F_89(x), F_12(x)*F_62(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_98(x))
Eq(F_92(x), F_23(x) + F_93(x))
Eq(F_93(x), F_18(x) + F_94(x) + F_97(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_20(x) + F_96(x))
Eq(F_96(x), F_56(x) + F_93(x))
Eq(F_97(x), F_12(x)*F_92(x))
Eq(F_98(x), F_106(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_104(x) + F_18(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_14(x) + F_40(x))
Eq(F_103(x), F_27(x) + F_68(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_23(x) + F_99(x))
Eq(F_106(x), F_107(x) + F_111(x) + F_113(x) + F_18(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_17(x) + F_43(x))
Eq(F_110(x), F_56(x) + F_80(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_106(x) + F_93(x))
Eq(F_113(x), F_12(x)*F_98(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, 2, 3, 1], "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, 1, 2, 0], "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, 2, 3, 1], "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, 1, 2, 0], "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, 2, 3, 1], "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, 1, 2, 0], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "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, 2, 0], "pos": [[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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 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], "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, 2, 0], "pos": [[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, 2, 0], "pos": [[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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 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": [[1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": 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