02341_02413_02431_03241_20341_20413_20431_23041_30241_32041
Counting sequence:
1, 1, 2, 6, 24, 110, 542, 2790, 14810, 80464, 445264, 2500894, 14220646, 81703378, 473581934, 2766040842, 16263183278, 96180720584, 571764730932, 3414691895032, 20477906301440, 123266301752652, 744521480560460, 4510798688579286, 27406838303166334, 166952746701239684, 1019457086223947164, 6238880570365620770, 38259286367583511342, 235069885015761508278, 1446874542544347479762, 8920472051109194835674, 55083563358941721422246, 340637000056875302300746, 2109401785906210841434710, 13079462108374870228561248, 81199218874181279613975040, 504680030980026007947539892, 3140190005336021897518434660, 19558997290413976478886944624, 121945362660718100297066782116, 761010964549376188914170705858, 4753394542143892958632633190986, 29715697058364413746295809612524, 185917440347592399558769947184716, 1164101030971985842625194990892744, 7294285774402771985247272964356936, 45738572835938463598971786067965950, 286996915707621975498329559508462930, 1801998746880897262686869355458960760, 11321473668077676627804034706897448132, 71172450924783024569072105507190908764, 447683672839514619043630549872143109480, 2817548687800951246433677087609637750640, 17742035465102907979701841314258700182304, 111778632469609533205482480995772663793154, 704578572670348823340389311585765966549882, 4443321553331955747343427298210807812489248, 28034092807277940103706826248164400978492328, 176953383497312537594147530587895041264245510, 1117424864918446976766342773706427433448599330, 7059252292265633946539376525756555504775962474, 44614302444688963456351607130519995993020386878, 282071327474623270357452897187932002697126288642, 1784053503389076786569793097690308721950115823534, 11287969231068173814715110004940155456081707080954, 71445999364187569746404607231519521764987794489618, 452365561673496670742606542997853100984527369816258, 2865142629661932498628627728962718140350942463712938, 18152808023854009747122599429175904600014367495837130, 115047765330229482277333123088356910005357752241351526, 729365949439363487125890074910104982205513723168283384, 4625322169699871978081586087995512642165659498942879712, 29340271993284297609251203837386224357727637150400152840, 186169489642686390170518769229199120095898340262840728176, 1181603654742185111670460639286688347518415786887556675268, 7501548777859499820040121382153109638668597459271957867672, 47636826028670758282343754927431293154466125900951334014068, 302583021625537456191122672664798672194813716474436084201140, 1922442475509160483400104208128116349743149041139122680978008, 12217054702301996812065962275986954315219755749612925904766536, 77657151786913050947164608634565133329028667263437468581113108, 493737001199878040615536387147743679281647886886234437793777744, 3139834542805114976139885618327105532352021967513267498408079650, 19971578989284174299611141394030933309833249523836284977769359498, 127060440120888448433200847195965767526418493116721887967579499582, 808534327048856542240115966906311484453100057846820920885112872458, 5146057578004383874196103811063477528982269614804891626273796337188, 32759470759977691201040888129863688460945441845011331080953893081744, 208585073149324244058315398075003110528025362819113354101529824052742, 1328347824917969301021045607368111823159207669181408874169794983191374, 8460982731513712599976451652423700231548142564921574222973943427529096, 53902445317573691344386626674566905565718010628447906692951283354844036, 343457564083630947010464438956350582742266530536855479006706159226796132, 2188834956844893193421498275275409469901521888757482836489891033527713876, 13951685110372624035216693580150667658251399686123343513387170089103806974, 88943146816266974843114449561798781121679874118885819460176645139789379770, 567112207123270889733871865534462868696492074662407249052057389586502139610, 3616552138322605280930683562263511027199235591642878968806661777509507916430, 23066849921027551947581644860421655996604175757763508407015822667598346511168, 147145949211551536895048620301643760455637284738482312369143690735334473859444
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24230/
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[33,x]+F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[22,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[11,x,k[0]]*F[9,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[19,x,k[0]]+F[22,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,1,k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[9,x]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]+F[6,x,k[1]]
F[17,x,k[0],k[1]] = F[12,x,k[1]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[12,x,k[0]]*F[21,x]*F[9,x]
F[21,x] = F[1,x]+F[9,x]
F[22,x,k[0]] = F[18,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,1,k[0]]*k[0]-F[24,x,1/k[0],k[0]])
F[24,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[27,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[18,x,k[1]]*F[24,x,k[0],k[1]]*F[29,x,k[1]]
F[29,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[30,x,k[0],k[1]] = F[31,x,k[0]*k[1],k[1]]
F[31,x,k[0],k[1]] = F[18,x,k[1]]*F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = (-F[24,x,1,k[1]]*k[1]+F[24,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[33,x] = F[34,x]*F[9,x]
F[34,x] = F[12,x,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{22}\! \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_{11}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = \frac{y F_{12}\! \left(x , y\right)-F_{12}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , 1, y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right)+F_{6}\! \left(x , z\right)
F_{17}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{21}\! \left(x \right) F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = \frac{y F_{24}\! \left(x , 1, y\right)-F_{24}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{24}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{18}\! \left(x , z\right) F_{24}\! \left(x , y , z\right) F_{29}\! \left(x , z\right)
F_{29}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{30}\! \left(x , y , z\right) = F_{31}\! \left(x , y z , z\right)
F_{31}\! \left(x , y , z\right) = F_{18}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = \frac{-z F_{24}\! \left(x , 1, z\right)+y F_{24}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{9}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x , 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_9(x))
Eq(F_3(x), F_1(x) + F_33(x) + F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_22(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_11(x, k_0)*F_9(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_19(x, k_0) + F_22(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, 1, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_9(x))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1) + F_6(x, k_1))
Eq(F_17(x, k_0, k_1), F_12(x, k_1)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_12(x, k_0)*F_21(x)*F_9(x))
Eq(F_21(x), F_1(x) + F_9(x))
Eq(F_22(x, k_0), F_18(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), (k_0*F_24(x, 1, k_0) - F_24(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_24(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_27(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_18(x, k_1)*F_24(x, k_0, k_1)*F_29(x, k_1))
Eq(F_29(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_30(x, k_0, k_1), F_31(x, k_0*k_1, k_1))
Eq(F_31(x, k_0, k_1), F_18(x, k_1)*F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), (-k_0*F_24(x, k_0/k_1, k_1) + k_1*F_24(x, 1, k_1))/(-k_0 + k_1))
Eq(F_33(x), F_34(x)*F_9(x))
Eq(F_34(x), F_12(x, 1))
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, 2, 3, 4, 1], "pos": [[0, 0], [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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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