0132_0213_0231_1302_3012
Counting sequence:
1, 1, 2, 6, 19, 56, 161, 459, 1302, 3676, 10331, 28908, 80567, 223731, 619274, 1709106, 4704451, 12918464, 35397197, 96797691, 264223326, 720030088, 1959112907, 5322888756, 14443047779, 39141157731, 105951640466, 286492505694, 773890887667, 2088496448456, 5631182320121, 15170485808043, 40836997130022, 109845236363956, 295256182281659, 793090990658556, 2128962359906831, 5711465119522899, 15313494519831962, 41035533973022346, 109904592477213091, 294206183159501648, 787186291025968037, 2105241752291546331, 5627733818943426414, 15037655201449855456, 40165123423044752171, 107237694483689115204, 286208006638398123707, 763586485846627132611, 2036491885536473373986, 5429510314252641412278, 14470962053056006031827, 38556523688929193767256, 102699129549938471353169, 273469278725493091457931, 727993427384154520434486, 1937436751935204750921484, 5154809353188548858144027, 13711543133423474919876876, 36462982999693886064771431, 96942342897701180667925683, 257675693836926637956185642, 684754746011586681858683106, 1819286918249840271576839299, 4832531123495446776084709856, 12833883422457031122358939901, 34076424939779727144824183739, 90461731814373860907928183422, 240100485959912906812572009016, 637148532017586302634808199051, 1690479812492939279173302011988, 4484386206709289926024425753107, 11893830008979012394236509572131, 31540462123011934551555378021554, 83626480067065271249703915342606, 221692390896425131870508965498291, 587612007369925402391406482778344, 1557274162638255656719508390223017, 4126440760071840033984928908423531, 10932608424733355262472911089259846, 28960835156069499738928892401460068, 76707688662142875093561397487220347, 203146155044421044974003106134396956, 537924757494638286985943707766458559, 1424226136295985978024067571642246931, 3770353726939278106049481883741598906, 9980037252303231554973807154849231674, 26413764577768607744457003930024825187, 69900073916615782020302968607614749296, 184958902931120118156584129460769209941, 489355154718255521627940338506152736923, 1294569674989137914422577414684118782862, 3424364691704121675547322572694033101456, 9057093750722626006246641776215039208939, 23952613790806989571366826507254431097956, 63339269962128643498349257526641235115371, 167475065886526610066992981664644870766979, 442777014729863893342070374462127185711682, 1170519369609355520734228167114262515427686, 3094080180984661314546203516063404039224211
Generating function in Maple syntax:
-(2*x^7-6*x^6+4*x^5-9*x^4+20*x^3-18*x^2+7*x-1)/(x^2-3*x+1)^2/(x-1)^2
Generating function in latex syntax:
-\frac{2 x^{7}-6 x^{6}+4 x^{5}-9 x^{4}+20 x^{3}-18 x^{2}+7 x -1}{\left(x^{2}-3 x +1\right)^{2} \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-2*x**7 + 6*x**6 - 4*x**5 + 9*x**4 - 20*x**3 + 18*x**2 - 7*x + 1)/((x - 1)**2*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)^2*(x-1)^2*F(x)+2*x^7-6*x^6+4*x^5-9*x^4+20*x^3-18*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)+2 x^{7}-6 x^{6}+4 x^{5}-9 x^{4}+20 x^{3}-18 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/50*((10*n-163)*5^(1/2)-20*n+375)*(3/2-1/2*5^(1/2))^(-n)+1/50*((-10*n+163)*5^(1/2)-20*n+375)*(3/2+1/2*5^(1/2))^(-n)+n-4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(\left(10 n -163\right) \sqrt{5}-20 n +375\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{50}+\\\frac{\left(\left(-10 n +163\right) \sqrt{5}-20 n +375\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{50}+n -4 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 161
a(7) = 459
a(n+4) = -a(n)+6*a(n+1)-11*a(n+2)+6*a(n+3)+n-2, 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 161
a \! \left(7\right) = 459
a \! \left(n +4\right) = -a \! \left(n \right)+6 a \! \left(n +1\right)-11 a \! \left(n +2\right)+6 a \! \left(n +3\right)+n -2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21580/
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[8,x]
F[4,x] = F[40,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = 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[8,x]
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[8,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[8,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[8,x]
F[24,x] = F[19,x]
F[25,x] = F[14,x]*F[8,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[28,x]*F[8,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[8,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = 2*F[20,x]+F[34,x]+F[38,x]
F[34,x] = F[35,x]*F[8,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[26,x]*F[8,x]
F[39,x] = F[13,x]*F[8,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]*F[8,x]
F[42,x] = F[120,x]+F[43,x]
F[43,x] = F[44,x]+F[78,x]
F[44,x] = F[45,x]+F[59,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]*F[8,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[49,x]*F[8,x]
F[52,x] = F[46,x]+F[53,x]
F[53,x] = F[20,x]+F[54,x]+F[58,x]
F[54,x] = F[55,x]*F[8,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[50,x]
F[57,x] = F[53,x]
F[58,x] = F[52,x]*F[8,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = F[20,x]+F[61,x]+F[66,x]
F[61,x] = F[62,x]*F[8,x]
F[62,x] = F[50,x]+F[63,x]
F[63,x] = F[20,x]+F[61,x]+F[64,x]
F[64,x] = F[65,x]*F[8,x]
F[65,x] = F[50,x]+F[63,x]
F[66,x] = F[67,x]*F[8,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[50,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[68,x]*F[8,x]
F[71,x] = F[60,x]+F[72,x]
F[72,x] = 2*F[20,x]+F[73,x]+F[77,x]
F[73,x] = F[74,x]*F[8,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[69,x]
F[76,x] = F[72,x]
F[77,x] = F[71,x]*F[8,x]
F[78,x] = F[102,x]+F[79,x]
F[79,x] = F[50,x]+F[80,x]
F[80,x] = F[20,x]+F[81,x]+F[94,x]
F[81,x] = F[8,x]*F[82,x]
F[82,x] = F[83,x]+F[89,x]
F[83,x] = F[84,x]
F[84,x] = F[8,x]*F[85,x]
F[85,x] = F[17,x]+F[86,x]
F[86,x] = F[50,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[50,x]*F[8,x]
F[89,x] = F[20,x]+F[81,x]+F[90,x]
F[90,x] = F[8,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[50,x]
F[93,x] = F[63,x]
F[94,x] = F[8,x]*F[95,x]
F[95,x] = F[68,x]+F[96,x]
F[96,x] = F[80,x]+F[97,x]
F[97,x] = 2*F[20,x]+F[101,x]+F[98,x]
F[98,x] = F[8,x]*F[99,x]
F[99,x] = F[100,x]+F[75,x]
F[100,x] = F[97,x]
F[101,x] = F[8,x]*F[96,x]
F[102,x] = F[103,x]+F[107,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[8,x]
F[105,x] = F[106,x]+F[8,x]
F[106,x] = F[104,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[8,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[103,x]+F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[110,x]*F[8,x]
F[113,x] = F[107,x]+F[114,x]
F[114,x] = 3*F[20,x]+F[115,x]+F[119,x]
F[115,x] = F[116,x]*F[8,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[111,x]
F[118,x] = F[114,x]
F[119,x] = F[113,x]*F[8,x]
F[120,x] = F[121,x]*F[6,x]
F[121,x] = F[122,x]+F[44,x]
F[122,x] = F[59,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{40}\! \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_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
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_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{42}\! \left(x \right) = F_{120}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{78}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{59}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right) F_{8}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49}\! \left(x \right) F_{8}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right)+F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right)+F_{61}\! \left(x \right)+F_{66}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{8}\! \left(x \right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right)+F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right) F_{8}\! \left(x \right)
F_{65}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right) F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{50}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right) F_{8}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right) F_{8}\! \left(x \right)
F_{78}\! \left(x \right) = F_{102}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{50}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right)+F_{81}\! \left(x \right)+F_{94}\! \left(x \right)
F_{81}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{89}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{8}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{17}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{50}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{81}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{8}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{50}\! \left(x \right)
F_{93}\! \left(x \right) = F_{63}\! \left(x \right)
F_{94}\! \left(x \right) = F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{68}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{80}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{8}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{75}\! \left(x \right)
F_{100}\! \left(x \right) = F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{107}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{8}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{8}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{8}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{110}\! \left(x \right) F_{8}\! \left(x \right)
F_{113}\! \left(x \right) = F_{107}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{8}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{111}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right)
F_{119}\! \left(x \right) = F_{113}\! \left(x \right) F_{8}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{6}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{44}\! \left(x \right)
F_{122}\! \left(x \right) = F_{59}\! \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_8(x))
Eq(F_4(x), F_40(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_8(x)*F_9(x))
Eq(F_8(x), 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_8(x))
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_8(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_8(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_8(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_14(x)*F_8(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_28(x)*F_8(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_8(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), 2*F_20(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_35(x)*F_8(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_26(x)*F_8(x))
Eq(F_39(x), F_13(x)*F_8(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x)*F_8(x))
Eq(F_42(x), F_120(x) + F_43(x))
Eq(F_43(x), F_44(x) + F_78(x))
Eq(F_44(x), F_45(x) + F_59(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x)*F_8(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_49(x)*F_8(x))
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), F_20(x) + F_54(x) + F_58(x))
Eq(F_54(x), F_55(x)*F_8(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_50(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_52(x)*F_8(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_20(x) + F_61(x) + F_66(x))
Eq(F_61(x), F_62(x)*F_8(x))
Eq(F_62(x), F_50(x) + F_63(x))
Eq(F_63(x), F_20(x) + F_61(x) + F_64(x))
Eq(F_64(x), F_65(x)*F_8(x))
Eq(F_65(x), F_50(x) + F_63(x))
Eq(F_66(x), F_67(x)*F_8(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_50(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_68(x)*F_8(x))
Eq(F_71(x), F_60(x) + F_72(x))
Eq(F_72(x), 2*F_20(x) + F_73(x) + F_77(x))
Eq(F_73(x), F_74(x)*F_8(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_69(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_71(x)*F_8(x))
Eq(F_78(x), F_102(x) + F_79(x))
Eq(F_79(x), F_50(x) + F_80(x))
Eq(F_80(x), F_20(x) + F_81(x) + F_94(x))
Eq(F_81(x), F_8(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_89(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_8(x)*F_85(x))
Eq(F_85(x), F_17(x) + F_86(x))
Eq(F_86(x), F_50(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_50(x)*F_8(x))
Eq(F_89(x), F_20(x) + F_81(x) + F_90(x))
Eq(F_90(x), F_8(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_50(x))
Eq(F_93(x), F_63(x))
Eq(F_94(x), F_8(x)*F_95(x))
Eq(F_95(x), F_68(x) + F_96(x))
Eq(F_96(x), F_80(x) + F_97(x))
Eq(F_97(x), F_101(x) + 2*F_20(x) + F_98(x))
Eq(F_98(x), F_8(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_75(x))
Eq(F_100(x), F_97(x))
Eq(F_101(x), F_8(x)*F_96(x))
Eq(F_102(x), F_103(x) + F_107(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_8(x))
Eq(F_105(x), F_106(x) + F_8(x))
Eq(F_106(x), F_104(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_8(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_103(x) + F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_110(x)*F_8(x))
Eq(F_113(x), F_107(x) + F_114(x))
Eq(F_114(x), F_115(x) + F_119(x) + 3*F_20(x))
Eq(F_115(x), F_116(x)*F_8(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_111(x))
Eq(F_118(x), F_114(x))
Eq(F_119(x), F_113(x)*F_8(x))
Eq(F_120(x), F_121(x)*F_6(x))
Eq(F_121(x), F_122(x) + F_44(x))
Eq(F_122(x), F_59(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 1, 3], "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, 3, 0, 2], "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, 2, 1, 3], "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, 3, 0, 2], "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, 2, 1, 3], "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, 3, 0, 2], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "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": [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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 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