0123_02413_03412_12403_13402_23401

Counting sequence:
1, 1, 2, 6, 23, 98, 434, 1949, 8803, 39888, 181201, 825201, 3767757, 17249560, 79191480, 364585230, 1683208515, 7792546040, 36174065285, 168367375735, 785637327745, 3674914227120, 17230132657815, 80965662243526, 381275131584373, 1799105397745998, 8505728881799069, 40286635890904809, 191145654448095787, 908412406974291252, 4323943749199891014, 20612014717370081389, 98394604327654578963, 470328656490378137376, 2251031782957272245693, 10786593457357006445343, 51746816152474972117809, 248516556946968894564824, 1194748860206978274289635, 5749448233255998117607260, 27693887645716808847905345, 133515321767432986196458470, 644243546416956779174046465, 3111173872014653150136933885, 15036202939207227230614386255, 72723898979496231980102782380, 351987689636763393246422539365, 1704810898357289732000800022265, 8262494795868622555047118208253, 40070149612733775263418369005238, 194444065437689215133983850661981, 944109086692201894158512292228231, 4586630733607639312384652257868487, 22294635467996670906208598694375596, 108425978690134231870818887386886843, 527575400041851030849360602247635668, 2568302625192249554994780012816747019, 12508665767499727138026613440170785134, 60949752832132048219187569973229583503, 297113551018341662430495487947543298963, 1448959447981147868965053530505181013701, 7069151303046188070051002052928091497076, 34502447182521733000718528041233941190032, 168460726574856289780695393047209314955950, 822826763875261324254925417298313359872275, 4020445505516892687072974479538408260094400, 19651299036053819607023498251432853548097325, 96084903087911823723547873174525364279185575, 469960705855963575689366623028972945811331425, 2299356522658103626706216104753434021680911800, 11253445547955163582273403146294679576020352475, 55092865720672800225075398943482834776327818100, 269793971165600288222770602108347410840088287825, 1321577607664466505619371408614011894872717479510, 6475500211006548926279254212014556337484738243105, 31737374082004870163124364655933747287316744935605, 155590330584574533884892419076885604997011598932815, 762966034827064967020744343500996629838359848383340, 3742277191522726736707674920583957440030024093000945, 18359976168059699073276635060797650926260785607782095, 90097150220987894815836799551588388893745328953478665, 442232078529861268768643231447717645282028290954516790, 2171137029330392271722922933340071090280736046349604305, 10661533541783741817013817282763165628299998118487547835, 52365505686699939692107121447032108930945773561210808155, 257253870363734438623525093985866178492718964856418232780, 1264059191367420118651188493971893972287610669002008633015, 6212404727792763220429823933468672413602181718044604790540, 30537743165412001678702864594165932744200484406317627997775, 150140236625485452300317794669009556892022399608751186578150, 738309358744324577864380705054016773609808509758957726438675, 3631273748627531040809792995828650099667006395310841825626175, 17863116175328563443064041588565694256813637501875571213710225, 87888368853769152602553368248763433341982589118719754339424900, 432493834597772633103107872259628721029744201608121150929865575, 2128635049375061744138041264629185985746418740563847743353844950, 10478370588714762969751035147571139497504927819014863395523125725, 51588878760638954329215444421263757140777703861786931375599912350, 254031042639846978175367024570913136205467243031369127479733096285, 1251078266625645116122900939206346286680217321776209356083040766735, 6162370667179476267700017503162425747376568036823850797084190554695

Implicit equation for the generating function in Maple syntax:
(x-1)^2*x^5*F(x)^4-2*x^3*(4*x-1)*(x-1)^2*F(x)^3+x*(x-1)*(2*x^4+15*x^3-28*x^2+10*x-1)*F(x)^2-(x-1)*(4*x-1)*(2*x^3-x^2-4*x+1)*F(x)+x^5+4*x^4-21*x^3+25*x^2-9*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{2} x^{5} F \! \left(x \right)^{4}-2 x^{3} \left(4 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)^{3}+x \left(x -1\right) \left(2 x^{4}+15 x^{3}-28 x^{2}+10 x -1\right) F \! \left(x \right)^{2}-\left(x -1\right) \left(4 x -1\right) \left(2 x^{3}-x^{2}-4 x +1\right) F \! \left(x \right)+x^{5}+4 x^{4}-21 x^{3}+25 x^{2}-9 x +1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 23
a(5) = 98
a(6) = 434
a(n+7) = -100*(n+1)*(2*n+1)/(n+9)/(n+8)*a(n)+10*(17*n+30)*(n-1)/(n+9)/(n+8)*a(n+1)+2*(287*n^2+2157*n+3880)/(n+9)/(n+8)*a(n+2)-(975*n^2+8471*n+18196)/(n+9)/(n+8)*a(n+3)+2*(283*n^2+2999*n+7860)/(n+9)/(n+8)*a(n+4)-2*(77*n^2+975*n+3058)/(n+9)/(n+8)*a(n+5)+4*(5*n+34)/(n+9)*a(n+6), n >= 7

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) = 23
a \! \left(5\right) = 98
a \! \left(6\right) = 434
a \! \left(n +7\right) = -\frac{100 \left(n +1\right) \left(2 n +1\right) a \! \left(n \right)}{\left(n +9\right) \left(n +8\right)}+\frac{10 \left(17 n +30\right) \left(n -1\right) a \! \left(n +1\right)}{\left(n +9\right) \left(n +8\right)}+\frac{2 \left(287 n^{2}+2157 n +3880\right) a \! \left(n +2\right)}{\left(n +9\right) \left(n +8\right)}-\frac{\left(975 n^{2}+8471 n +18196\right) a \! \left(n +3\right)}{\left(n +9\right) \left(n +8\right)}+\frac{2 \left(283 n^{2}+2999 n +7860\right) a \! \left(n +4\right)}{\left(n +9\right) \left(n +8\right)}-\frac{2 \left(77 n^{2}+975 n +3058\right) a \! \left(n +5\right)}{\left(n +9\right) \left(n +8\right)}+\frac{4 \left(5 n +34\right) a \! \left(n +6\right)}{n +9}, \quad n \geq 7

Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24083/
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[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[12,x,k[0]]*F[7,x,k[0]]
F[7,x,k[0]] = F[10,x,k[0]]+F[5,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]*F[30,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[13,x,k[0]]*F[27,x]*F[3,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[5,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[19,x,k[0]]+F[25,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[18,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[20,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[21,x,k[0]]+F[23,x,k[0]]
F[20,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
F[21,x,k[0]] = F[22,x,k[0]]*F[3,x]
F[22,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[23,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[24,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x]^2*F[3,x]*F[30,x,k[0]]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[27,x]*F[3,x]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[12,x,k[0]]*F[30,x,k[0]]
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\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{5}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27} \left(x \right)^{2} F_{3}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{30}\! \left(x , y\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_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_12(x, k_0)*F_7(x, k_0))
Eq(F_7(x, k_0), F_10(x, k_0) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x, k_0)*F_30(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_13(x, k_0)*F_27(x)*F_3(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_5(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_19(x, k_0) + F_25(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_18(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_1(x) + F_19(x, k_0) + F_21(x, k_0) + F_23(x, k_0))
Eq(F_20(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_3(x))
Eq(F_22(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_23(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_24(x, k_0), (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x)**2*F_3(x)*F_30(x, k_0))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_27(x)*F_3(x))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_12(x, k_0)*F_30(x, k_0))
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": 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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_and_col_placements_tracked_fusion_req_corrob_expand_verified", "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "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": [[1, 3]]}]}], "class_module": "tilings.tiling", 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"pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 3]], [[1, 2]], [[2, 1]], [[3, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], 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"strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": 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3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 2]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "ReverseRule"}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}

Specification 2
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/24084/
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[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[14,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[12,x,k[0]]+F[6,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]*F[32,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[15,x,k[0]]*F[29,x]*F[4,x]
F[16,x,k[0]] = F[17,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]+F[6,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[21,x,k[0]]+F[27,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[4,x]
F[20,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[22,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[23,x,k[0]]+F[25,x,k[0]]
F[22,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[23,x,k[0]] = F[24,x,k[0]]*F[4,x]
F[24,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x]^2*F[32,x,k[0]]*F[4,x]
F[29,x] = F[1,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[29,x]*F[4,x]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[14,x,k[0]]*F[32,x,k[0]]
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29} \left(x \right)^{2} F_{32}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{32}\! \left(x , y\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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_14(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_12(x, k_0) + F_6(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_15(x, k_0)*F_32(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_15(x, k_0)*F_29(x)*F_4(x))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0) + F_6(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_21(x, k_0) + F_27(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_4(x))
Eq(F_20(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_22(x, k_0), F_1(x) + F_21(x, k_0) + F_23(x, k_0) + F_25(x, k_0))
Eq(F_22(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_4(x))
Eq(F_24(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x)**2*F_32(x, k_0)*F_4(x))
Eq(F_29(x), F_1(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_29(x)*F_4(x))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_14(x, k_0)*F_32(x, k_0))
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"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "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": "point_and_row_and_col_placements_tracked_fusion_expand_verified", "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "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": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 3], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 3], [1, 0], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 3], [1, 2], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 0], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 0], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 3], [1, 2], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 0], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 0], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 2], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 2], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 0], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 2], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 3], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 4], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 4], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 2], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 2], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 3], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 3]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 3]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 0], [1, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 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