0132_0231_1203_1230_3120
Counting sequence:
1, 1, 2, 6, 19, 59, 176, 501, 1363, 3563, 9006, 22141, 53209, 125507, 291516, 668485, 1516511, 3409035, 7603530, 16844317, 37095173, 81266691, 177211672, 384830021, 832572299, 1795165419, 3858763366, 8271171581, 17683190193, 37715186563, 80262206836, 170456520581, 361314130359, 764504185867, 1614907711106, 3405909074205, 7172595393501, 15083925153475, 31679678786000, 66451734015237, 139225659879523, 291370581373931, 609129441802142, 1272134953352061, 2654221069467529, 5532742510986179, 11522881859110956, 23978149578558661, 49856255249895823, 103582791429543563, 215046882206964666, 446137838086414621, 924926773471241909, 1916281641446173827, 3967671271713436296, 8210062120696445125, 16978570595186802491, 35092048296470939115, 72489939602155539670, 149663622816776360957, 308838848046559173473, 636989131295282995971, 1313177593747198749412, 2705906771312269898501, 5573222553269498329959, 11473874813847341155339, 23611832414348226120946, 48570277146077249459741, 99870672415063512506253, 205275368052239890442563, 421766356501295188210496, 866259101701400543952261, 1778561276610780128675859, 3650389291258235750257387, 7489673241831257308995086, 15361858168774955880229245, 31498184440740533575431481, 64564194553793789361733955, 132301819384075980306992540, 271026057184854678104529477, 555048066930566619837065023, 1136390270437751424223900811, 2325973276938546532134781482, 4759540951822795060818317341, 9736688551176223373083647589, 19913426100692171765760240899, 40716621604620710604104121336, 83232124828827989420170922821, 170100698523056783397857909483, 347551666029370512177929251563, 709958612530165587654647872326, 1449937271013001646975599381501, 2960533603950986927421255720209, 6043623271791226502057524604547, 12334834551439529059094873915476, 25169796878750351749248993874565, 51349752829557573802815672968471, 104739630843857454298665102505995, 213599126138456654152194490272610, 435517209340911063751711095168797, 887830789134846167073253507642173
Generating function in Maple syntax:
-(x^7+8*x^6-44*x^5+76*x^4-68*x^3+34*x^2-9*x+1)/(2*x-1)^3/(x-1)^4
Generating function in latex syntax:
-\frac{x^{7}+8 x^{6}-44 x^{5}+76 x^{4}-68 x^{3}+34 x^{2}-9 x +1}{\left(2 x -1\right)^{3} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**7 - 8*x**6 + 44*x**5 - 76*x**4 + 68*x**3 - 34*x**2 + 9*x - 1)/((x - 1)**4*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(x-1)^4*F(x)+x^7+8*x^6-44*x^5+76*x^4-68*x^3+34*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(x -1\right)^{4} F \! \left(x \right)+x^{7}+8 x^{6}-44 x^{5}+76 x^{4}-68 x^{3}+34 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/48*(3*n^2+39*n-282)*2^n+1/6*n^3+n^2+17/6*n+7)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(3 n^{2}+39 n -282\right) 2^{n}}{48}+\frac{n^{3}}{6}+n^{2}+\frac{17 n}{6}+7 & \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) = 59
a(6) = 176
a(7) = 501
a(n+3) = -1/6*n^3+1/2*n^2+8*a(n)-12*a(n+1)+6*a(n+2)+5/3*n-3, 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) = 59
a \! \left(6\right) = 176
a \! \left(7\right) = 501
a \! \left(n +3\right) = -\frac{n^{3}}{6}+\frac{n^{2}}{2}+8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)+\frac{5 n}{3}-3, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18942/
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[96,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[50,x]
F[35,x] = F[36,x]+F[6,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[14,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[39,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[14,x]+F[43,x]
F[46,x] = 2*F[18,x]+F[47,x]+F[49,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[40,x]+F[46,x]
F[49,x] = F[12,x]*F[42,x]
F[50,x] = F[32,x]+F[51,x]
F[51,x] = 2*F[18,x]+F[52,x]+F[56,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[36,x]
F[55,x] = F[51,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[65,x]
F[58,x] = F[27,x]+F[59,x]
F[59,x] = 2*F[18,x]+F[60,x]+F[64,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[40,x]
F[63,x] = F[59,x]
F[64,x] = F[12,x]*F[58,x]
F[65,x] = F[66,x]+F[78,x]
F[66,x] = 2*F[18,x]+F[67,x]+F[76,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[43,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[43,x]
F[75,x] = F[71,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[27,x]+F[66,x]
F[78,x] = 2*F[18,x]+F[79,x]+F[93,x]+F[95,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]+F[85,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[43,x]+F[82,x]
F[85,x] = F[86,x]
F[86,x] = 3*F[18,x]+F[87,x]+F[91,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[82,x]
F[90,x] = F[86,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[71,x]+F[86,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[59,x]+F[78,x]
F[95,x] = F[12,x]*F[65,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[105,x]+F[98,x]
F[98,x] = F[23,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[10,x]+F[40,x]
F[103,x] = F[59,x]+F[99,x]
F[104,x] = F[12,x]*F[98,x]
F[105,x] = F[106,x]+F[113,x]
F[106,x] = F[107,x]+F[111,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[14,x]+F[43,x]
F[110,x] = F[27,x]+F[71,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[106,x]+F[23,x]
F[113,x] = F[114,x]+F[118,x]+F[120,x]+F[18,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[40,x]+F[82,x]
F[117,x] = F[59,x]+F[86,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[113,x]+F[99,x]
F[120,x] = F[105,x]*F[12,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_{96}\! \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_{50}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{36}\! \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_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{27}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{40}\! \left(x \right)
F_{63}\! \left(x \right) = F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{78}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{67}\! \left(x \right)+F_{76}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \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_{43}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{43}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{27}\! \left(x \right)+F_{66}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{79}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{43}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{71}\! \left(x \right)+F_{86}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{59}\! \left(x \right)+F_{78}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{105}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \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_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{103}\! \left(x \right) = F_{59}\! \left(x \right)+F_{99}\! \left(x \right)
F_{104}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{113}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \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_{14}\! \left(x \right)+F_{43}\! \left(x \right)
F_{110}\! \left(x \right) = F_{27}\! \left(x \right)+F_{71}\! \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_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{118}\! \left(x \right)+F_{120}\! \left(x \right)+F_{18}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{40}\! \left(x \right)+F_{82}\! \left(x \right)
F_{117}\! \left(x \right) = F_{59}\! \left(x \right)+F_{86}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{113}\! \left(x \right)+F_{99}\! \left(x \right)
F_{120}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \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_96(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_50(x))
Eq(F_35(x), F_36(x) + F_6(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_14(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_39(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_14(x) + F_43(x))
Eq(F_46(x), 2*F_18(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_40(x) + F_46(x))
Eq(F_49(x), F_12(x)*F_42(x))
Eq(F_50(x), F_32(x) + F_51(x))
Eq(F_51(x), 2*F_18(x) + F_52(x) + F_56(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_51(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_65(x))
Eq(F_58(x), F_27(x) + F_59(x))
Eq(F_59(x), 2*F_18(x) + F_60(x) + F_64(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_40(x))
Eq(F_63(x), F_59(x))
Eq(F_64(x), F_12(x)*F_58(x))
Eq(F_65(x), F_66(x) + F_78(x))
Eq(F_66(x), 2*F_18(x) + F_67(x) + F_76(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_43(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_43(x))
Eq(F_75(x), F_71(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_27(x) + F_66(x))
Eq(F_78(x), 2*F_18(x) + F_79(x) + F_93(x) + F_95(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_85(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_43(x) + F_82(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), 3*F_18(x) + F_87(x) + F_91(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_82(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_71(x) + F_86(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_59(x) + F_78(x))
Eq(F_95(x), F_12(x)*F_65(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_105(x) + F_98(x))
Eq(F_98(x), F_23(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_10(x) + F_40(x))
Eq(F_103(x), F_59(x) + F_99(x))
Eq(F_104(x), F_12(x)*F_98(x))
Eq(F_105(x), F_106(x) + F_113(x))
Eq(F_106(x), F_107(x) + F_111(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_14(x) + F_43(x))
Eq(F_110(x), F_27(x) + F_71(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_106(x) + F_23(x))
Eq(F_113(x), F_114(x) + F_118(x) + F_120(x) + F_18(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_40(x) + F_82(x))
Eq(F_117(x), F_59(x) + F_86(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_113(x) + F_99(x))
Eq(F_120(x), F_105(x)*F_12(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, 0, 3], "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, 0, 3], "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, 0, 3], "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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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": [1, 2, 0, 3], "pos": [[0, 0], [1, 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, 1, 2], "pos": [[0, 1], [0, 1], [2, 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": [1, 2, 0, 3], "pos": [[0, 1], [2, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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": [1, 2, 0, 3], "pos": [[0, 0], [1, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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": [1, 2, 0, 3], "pos": [[0, 0], [1, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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": [1, 2, 0, 3], "pos": [[0, 0], [1, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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": [1, 2, 0, 3], "pos": [[0, 0], [1, 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, 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