01342_03142_10342_13042_30142_31042
Counting sequence:
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Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24102/
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[9,x]
F[3,x] = F[1,x]+F[25,x]+F[4,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[11,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[11,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[10,x,k[1]]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[7,x,k[1]]
F[15,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[1,x]+F[17,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[18,x,k[0],k[1]] = (F[6,x,k[0]]*k[0]-F[6,x,k[1]]*k[1])/(-k[1]+k[0])
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[9,x]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])
F[21,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[9,x]
F[22,x,k[0],k[1]] = F[16,x,k[0]]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = (F[24,x,k[0],1]*k[0]-F[24,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[25,x] = F[5,x]*F[9,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = \frac{y F_{6}\! \left(x , y\right)-F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , 1, y\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y z , z\right)
F_{14}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , z\right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)
F_{15}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = \frac{y F_{6}\! \left(x , y\right)-z F_{6}\! \left(x , z\right)}{-z +y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{20}\! \left(x , y , z\right) = \frac{y F_{18}\! \left(x , y , z\right)-F_{18}\! \left(x , 1, z\right)}{-1+y}
F_{21}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = \frac{y F_{24}\! \left(x , y , 1\right)-z F_{24}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{24}\! \left(x , y , z\right) = F_{14}\! \left(x , y , y z \right)
F_{25}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \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)*F_9(x))
Eq(F_3(x), F_1(x) + F_25(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_11(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_11(x, k_0), F_12(x, k_0)*F_16(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_10(x, k_1) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_7(x, k_1))
Eq(F_15(x, k_0, k_1), F_14(x, k_0, k_1)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_1(x) + F_17(x, k_0, k_1) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), (-k_0*F_6(x, k_0) + k_1*F_6(x, k_1))/(-k_0 + k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_9(x))
Eq(F_20(x, k_0, k_1), (k_0*F_18(x, k_0, k_1) - F_18(x, 1, k_1))/(k_0 - 1))
Eq(F_21(x, k_0, k_1), F_20(x, k_0, k_1)*F_9(x))
Eq(F_22(x, k_0, k_1), F_16(x, k_0)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0, 1) + k_1*F_24(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_25(x), F_5(x)*F_9(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "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": "row_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 4, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[5, 1]]}]}], "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], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [3, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [3, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [4, 1], [4, 1]]}, 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