03241_03412_03421_30241_30412_30421_32041_32401_34012_34021_34201
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, 1524831750, 8348277636, 45946421502, 254062504188, 1410766557732, 7863526070976, 43981872758514, 246769406256708, 1388526164228364, 7833576838654440, 44301614143740804, 251103453421282792, 1426226511474610404, 8116400731065294084, 46272243349012312565, 264245918837510282298, 1511402546925080517750, 8657528111737752337540, 49660504949699021334006, 285230998269767803566060, 1640282170384822387415908, 9443808789932257989919152, 54432148329534802223495814, 314064205693137675126104492, 1813898557618826325557820900, 10486190902491724502787091512, 60675436378907865063339251116, 351382410176828793703873494552, 2036582165232136621175037811632, 11813067174731004173699168460984, 68572075525046298167213706688962, 398328912948873194436373813364004, 2315438220925659971252689663664988, 13468186510699453005828960604579176, 78389532700704287810944844803094700, 456529890188743772629919482174967640, 2660310561188043024800231995384614696, 15510929214993194348328530173849912512, 90484994925655097164540888784573405508, 528128990887630970239817033058909030216, 3084040156569815828520111474896608657944, 18018097383148861855204782171555817396368, 105317233323857114456738711088347500853496, 615863762637233386715555713084167053445072, 3602948031641232601061546318620913454398604, 21086924778690136675179427684014256972751508, 123465174476725835448609474922307700037185621, 723179374040313046343580238862573886622028922, 4237527618702041852163369225462770551320341334, 24839272997664166834847468560120354233806095236, 145653242325277691004756433542158573215713107622, 854381232960312069250922270765573014105862069580, 5013361820960476584334403145829875971689244235300, 29427132047195323795774596447283237466973590810064, 172784302747517594798354287638767211430861346651262, 1014832067689881307099930810122312254203835807929116, 5962300855073194291165355182503867351817883813281140, 35039654096333817345139048747296727152265239440893080, 205981640083180381091607826711088610564009563803240572, 1211202305019883772438645560636651254084858129850721592, 7123955037726453146682377704304715649798400901501241920, 41912050499032522644688792149013223187147143851982688456, 246641968036519530489992834026955812570091732503116776982, 1451785848542283446363209056320847129677067259199464763148, 8547575466562250840489759821576835974411410249714267014196, 50336790803847017824337316476914472342928647325415877488504, 296502108672870791059842748031827489294577961345231033219588, 1746897045741607175694584569071557488098530074563953052272136, 10294417137284375104877952893270234000586989465418260450724152, 60677669351019158430352226420893116538424335977561872478849024, 357722720752362014444372372616372784920970864747123529589828348, 2109369045426169472922404646247334724655379144890147125092791096, 12440705134879612882577885305477278875510214009174624648857445672, 73387459591442332531927950929488870582012785685892063856577458864, 432993374803063562896494350407766468543979062444086650672384574456, 2555179183679798034048415442244727617696012582846175955974962597552, 15081356823959205426722816664736612385645656081234231377982262469960, 89030068132751292199060113717891274176879410324989281721142687873960, 525664413168816268379577242311109788452059485949159829480533300386914, 3104233822753861057747011550092834098292202313819210127721190198429412, 18334653346156182599330765168741568434730775512881764902537969968946556, 108308340899624625224190175279542858061954310688165737400342825828802920, 639912464528427363384713874312826141635485413486198251727484486574871740, 3781353591094030008664252738390183857043163609248437599225214167180067192, 22348104504712924163537883807639275463021957863337851229771407035834784040, 132098976270016990310621039686659940472332892107718287458165575876617774176
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24250/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[22,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[36,x,k[0]]+F[38,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[30,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[29,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[22,x,k[1]]
F[17,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[22,x,k[1]]
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1]] = F[22,x,k[1]]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = (-F[15,x,1,k[1]]*k[1]+F[15,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[22,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (-F[27,x,1,k[1]]*k[1]+F[27,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[20,x,k[0]*k[1],k[1]]
F[28,x,k[0],k[1]] = F[23,x,k[0]*k[1],k[1]]
F[29,x,k[0],k[1]] = F[25,x,k[0]*k[1],k[1]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]*F[7,x]
F[31,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])/(-1+k[0])
F[32,x,k[0],k[1]] = F[22,x,k[1]]*F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]-F[24,x,1,k[1]])/(-1+k[0])
F[34,x,k[0],k[1]] = F[22,x,k[1]]*F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[0]-F[26,x,1,k[1]])/(-1+k[0])
F[36,x,k[0]] = F[22,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = 1/(-1+k[0])*(F[15,x,1,k[0]]*k[0]-F[15,x,1/k[0],k[0]])
F[38,x,k[0]] = F[22,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[27,x,1,k[0]]*k[0]-F[27,x,1/k[0],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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y\right) = \frac{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = F_{14}\! \left(x , y z , z\right)
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)
F_{17}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y z , z\right)
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = \frac{-F_{15}\! \left(x , 1, z\right) z +F_{15}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{25}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = \frac{-F_{27}\! \left(x , 1, z\right) z +F_{27}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{27}\! \left(x , y , z\right) = F_{20}\! \left(x , y z , z\right)
F_{28}\! \left(x , y , z\right) = F_{23}\! \left(x , y z , z\right)
F_{29}\! \left(x , y , z\right) = F_{25}\! \left(x , y z , z\right)
F_{30}\! \left(x , y , z\right) = F_{31}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{31}\! \left(x , y , z\right) = \frac{F_{12}\! \left(x , y , z\right) y -F_{12}\! \left(x , 1, z\right)}{-1+y}
F_{32}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = \frac{F_{24}\! \left(x , y , z\right) y -F_{24}\! \left(x , 1, z\right)}{-1+y}
F_{34}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{35}\! \left(x , y , z\right)
F_{35}\! \left(x , y , z\right) = \frac{F_{26}\! \left(x , y , z\right) y -F_{26}\! \left(x , 1, z\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = \frac{F_{15}\! \left(x , 1, y\right) y -F_{15}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = \frac{F_{27}\! \left(x , 1, y\right) y -F_{27}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_22(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_36(x, k_0) + F_38(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_30(x, k_0, k_1) + F_32(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_28(x, k_0, k_1) + F_29(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_22(x, k_1))
Eq(F_17(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_22(x, k_1))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_14(x, k_0, k_1)*F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1), F_22(x, k_1)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_15(x, k_0/k_1, k_1) + k_1*F_15(x, 1, k_1))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_22(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0/k_1, k_1) + k_1*F_27(x, 1, k_1))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_20(x, k_0*k_1, k_1))
Eq(F_28(x, k_0, k_1), F_23(x, k_0*k_1, k_1))
Eq(F_29(x, k_0, k_1), F_25(x, k_0*k_1, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1)*F_7(x))
Eq(F_31(x, k_0, k_1), (-k_0*F_12(x, k_0, k_1) + F_12(x, 1, k_1))/(1 - k_0))
Eq(F_32(x, k_0, k_1), F_22(x, k_1)*F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), (-k_0*F_24(x, k_0, k_1) + F_24(x, 1, k_1))/(1 - k_0))
Eq(F_34(x, k_0, k_1), F_22(x, k_1)*F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), (-k_0*F_26(x, k_0, k_1) + F_26(x, 1, k_1))/(1 - k_0))
Eq(F_36(x, k_0), F_22(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), (k_0*F_15(x, 1, k_0) - F_15(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_38(x, k_0), F_22(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), (k_0*F_27(x, 1, k_0) - F_27(x, 1/k_0, k_0))/(k_0 - 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, 3, 2, 4, 1], "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": [0, 3, 4, 2, 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, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 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]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": 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