01342_01423_01432_02341_02413_02431_03412_03421_12340_12430_13420

Counting sequence:
1, 1, 2, 6, 24, 109, 524, 2593, 13064, 66668, 343593, 1784849, 9331901, 49055099, 259050394, 1373372882, 7305871379, 38981009097, 208536689730, 1118243304822, 6009114036018, 32353143203047, 174493251750678, 942608664335210, 5099385352518836, 27624082391866118, 149829530892387125, 813593369228203393, 4422653736819822742, 24065384747799138033, 131071699171413040043, 714506099524736634289, 3898170783539526216134, 21283977855798022096407, 116295440834846293272390, 635876973162176443245188, 3479108959466451601865600, 19047271601900827233202100, 104340705519915830643367119, 571897872962671234489221906, 3136283450736637240087963008, 17208121964045286138759119362, 94463270238616653033224427257, 518793449008094291618453134164, 2850488511946038336534981021319, 15668566979754812986594967694464, 86162208164960523004620141005752, 473996116762493275584657912621101, 2608533788993111859453786768783346, 14360698643745604290796626696181818, 79087192421734571538621355827612107, 435695068759039698407352993254008787, 2401041962409076550152228244782072468, 13235869886282003650650256929215130122, 72985425657157497803266192303803434925, 402574490321241467539483912154416527879, 2221153510813436687077994626601771934811, 12258267590031199535929627980996342365267, 67669661382197809010678186398543134052583, 373654024897855938293770310144659838094305, 2063728823385906818932150191050987861607980, 11400912464224281398662667638649094867488381, 62998103439959418158996122367137590372992610, 348187545622847243083661540552637024257234361, 1924837318002139666475116049781536750464642303, 10643075443884906451174539315195440496269630512, 58861314684813260946657526754823136912593994802, 325596694942147436437454585153239762419312509952, 1801419428373647381814336380202734795451631103186, 9968555558139085361663277966654912812970036089044, 55173428067486943029303822195938358405794808003136, 305425956888525166284248275379351437828410755615364, 1691056576585080184157352867027375724731168441796765, 9364500402655667638854163350712614134151225201300816, 51866089352419049573917696086366448768069127969362784, 287311506353703826889287324095518348185166307412219919, 1591810752750501531678756833001708774729389840386151206, 8820578897263646569991651430243151013675301887341826374, 48884185717335032393415098130058122787241341826581304216, 270959126250738865199620377218333897910979770245727667705, 1502110208695451471387261083420716760734515102384661813336, 8328388905440089071251097486402358874194459409012058486735, 46182772265029344291237792925130561780850588491170357096512, 256128243270638824423823953465939890719361962903466439313313, 1420666446608645101130344276666575647182105324174789694903871, 7881025132732803330490506712761285932599537690912687277394590, 43724820476722474249620727693649910768746857737175795421431276, 242620184026132222776335225938817982090850888167388945421527362, 1346412904478957548061305886757948136484326294109272062033537964, 7472758700137188107568220936114926963596820290769557814391092062, 41479542131314489165688326943842247897709386250180177121949450327, 230269399944549781093701886442615519774478728017482392352394186556, 1278458973740661543093242281178138158175786819036198954747076439209, 7098795986026842813465860372547222298402324175048763220048431126224, 39421123476305024612660907127473116819516609261173369816639744427672, 218936817565213924185236041833026383063170681581446149384165621002570, 1216055039002795371442129098737444933754860334394797869615495855298314, 6755094682595008399224670359975030771326451979307757914900920805616647, 37527756674028011833630503350502140231935385657667207867474389060761585, 208504734845449012908791011494371831451542894020566384658949675195689282, 1158565565185112336525867679656803739333810774781755357466352916916512471

Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24240/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[38,x,k[0],k[1]]+F[41,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[3,x]
F[15,x,k[0],k[1]] = F[16,x,1,k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = F[1,x]+F[17,x,k[0],k[1],k[2]]+F[19,x,k[0],k[1],k[2]]+F[23,x,k[1],k[0],k[2]]+F[27,x,k[1],k[2],k[0]]
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[3,x]
F[18,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[16,x,k[0],k[1],k[2]]*k[0]-F[16,x,1,k[1],k[2]])
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[1],k[1]*k[2]]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[9,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],1,k[2]]*k[0]-F[22,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[22,x,k[0],k[1],k[2]] = (F[13,x,k[0],k[1]]*k[0]*k[1]-F[13,x,k[0],k[2]/k[0]]*k[2])/(k[0]*k[1]-k[2])
F[23,x,k[0],k[1],k[2]] = F[24,x,k[1],k[0],k[2]]*F[9,x,k[0]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = 1/(-1+k[2])*(F[26,x,k[0],k[1],k[2]]*k[2]-F[26,x,k[0],k[1],1])
F[26,x,k[0],k[1],k[2]] = F[12,x,k[0]*k[1],k[1]*k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[29,x,k[1],k[0]]*F[31,x,k[1]]*F[5,x,k[2]]*F[9,x,k[1]]
F[29,x,k[0],k[1]] = F[30,x,k[1]]+F[9,x,k[0]*k[1]]
F[30,x,k[0]] = F[1,x]+F[9,x,k[0]]
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[9,x,k[0]]
F[34,x,k[0]] = F[31,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[9,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[32,x,k[0]]*F[9,x,k[0]]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[0]*k[1]]
F[39,x,k[0],k[1]] = F[40,x,k[0],k[1]]*F[9,x,k[0]]
F[40,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[41,x,k[0],k[1]] = F[42,x,k[0],k[1]]
F[42,x,k[0],k[1]] = F[0,x]*F[29,x,k[1],k[0]]*F[31,x,k[1]]*F[9,x,k[1]]
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , 1, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{16}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{22}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{22}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} F_{13}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{13}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)}{y_{0} y_{1}-y_{2}}
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{25}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{26}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{1}, y_{0}\right) F_{31}\! \left(x , y_{1}\right) F_{5}\! \left(x , y_{2}\right) F_{9}\! \left(x , y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right)+F_{9}\! \left(x , y_{0} y_{1}\right)
F_{30}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{32}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{40}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{13}\! \left(x , y_{0}, 1\right)-y_{1} F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{0}\! \left(x \right) F_{29}\! \left(x , y_{1}, y_{0}\right) F_{31}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{1}\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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_38(x, k_0, k_1) + F_41(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_3(x))
Eq(F_15(x, k_0, k_1), F_16(x, 1, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), F_1(x) + F_17(x, k_0, k_1, k_2) + F_19(x, k_0, k_1, k_2) + F_23(x, k_1, k_0, k_2) + F_27(x, k_1, k_2, k_0))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_3(x))
Eq(F_18(x, k_0, k_1, k_2), (k_0*F_16(x, k_0, k_1, k_2) - F_16(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_1, k_1*k_2))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_9(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_0*F_22(x, k_0, 1, k_2) + k_1*F_22(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*k_1*F_13(x, k_0, k_1) + k_2*F_13(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_1, k_0, k_2)*F_9(x, k_0))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), (k_2*F_26(x, k_0, k_1, k_2) - F_26(x, k_0, k_1, 1))/(k_2 - 1))
Eq(F_26(x, k_0, k_1, k_2), F_12(x, k_0*k_1, k_1*k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_1, k_0)*F_31(x, k_1)*F_5(x, k_2)*F_9(x, k_1))
Eq(F_29(x, k_0, k_1), F_30(x, k_1) + F_9(x, k_0*k_1))
Eq(F_30(x, k_0), F_1(x) + F_9(x, k_0))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_9(x, k_0))
Eq(F_34(x, k_0), F_31(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_9(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_32(x, k_0)*F_9(x, k_0))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_0*k_1))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, k_1)*F_9(x, k_0))
Eq(F_40(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_0(x)*F_29(x, k_1, k_0)*F_31(x, k_1)*F_9(x, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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