1302_30241_304152_420531
Counting sequence:
1, 1, 2, 6, 23, 102, 492, 2498, 13130, 70800, 389446, 2176802, 12328552, 70597568, 408061604, 2377643974, 13950607135, 82355028006, 488797440712, 2915087969496, 17459865132260, 104981190319396, 633438776314456, 3834272763012274, 23277000755071712, 141687646777602412, 864580986739166552, 5287695648099792936, 32407211292172256756, 199006111610272154748, 1224284878057988228364, 7544621183804951283254, 46567603115651452546826, 287858364184739472246520, 1781899714029700590400470, 11044891291797905328676094, 68545792539647066997486672, 425903705106467463742453548, 2649267414360636737459574640, 16496758068917941746189541620, 102826829525186774935815190850, 641545803894249896406898335220, 4006288345992559020762323525552, 25039831711397734303378331728144, 156631073907220098802202122080272, 980540625653617892934235648400940, 6142982914326866621217426414665868, 38512787625745048343016724020240498, 241618016470948488959535814391332992, 1516840761519090449729314276187845596, 9528517646673723171075488028062425656, 59892773622900138675722512230376774152, 376683794614349558961804428724759861492, 2370408332016400177952976149283568981608, 14924642856159508480764457615282088634864, 94017917605400725260114445419088402663304, 592563669497847384358248477217631180555624, 3736537788403523788957679012361798953782256, 23572538781772143282543571193917541049598680, 148778096591907477682169160529238528045976440, 939421912591514901446654779315078151880684616, 5934240479444507965181543761057987239424932900, 37501305941007052147227638439042423531502473452, 237082092397543248170779930234742048830247051334, 1499397580527642055409583324931496347845732991327, 9486268055868212093873000613227462592794182360502, 60038465984827594158949581826262861458492671576680, 380114720686616640464644227483759388726515191026568, 2407388634266806466535624246397534460439078881826436, 15251755847069025760717611453082604605773138633591788, 96656596137303242937760537306310302491407088640197120, 612741409671449981348142507015856120679325594032635678, 3885556973040609585900704829152293003342786028114639488, 24646544386974910887894727738717696738162049165144281092, 156380297882299357992668563540396737917859685338112860296, 992494153219990570542047608391353379558996967742173536584, 6300726238504167381536364204679570109289340807799318036980, 40009850813546391394750080256046470152448093449556059251824, 254128853664386265266761795178520320521853150148592413358568, 1614540392839530457847371329568442483262373248760618169485444, 10260039184459952517371753262872787780689162463156440433897260, 65215626213734513455376554849999565092973668796400169306011120, 414623904695541957892306921509825532941353238860754625258862740, 2636662795846537879594850889563578302914829330436103999887100660, 16770657316119173330389427327335644882886894536331356692114753440, 106693645920070405440962504414358778836405035375543252146545873128, 678918780069484285442527635271730768933413647137505381870529032512, 4321015027747822952279820512015131368632022420349510062367250003656, 27506820001766375499189232087142205279082667523503654517316043829556, 175137716814965600056073312579800259713305199258774725090067930314168, 1115325861420198122640633656280343264592677401019103332445211416776128, 7104030478288883559981122592768586956603122785899833923023070087185040, 45257133088448052971549410238417902528500226663756583180604446275964872, 288367773566383048672254336393640816481436963242837604932046534415572284, 1837732133928324238733345070312628929925146416988958858881013083939096372, 11713640330026125931407914821985708665200004873662196189263107458233348210, 74674821329130729822197607613166224204427522857546055860604663124697711872, 476132274993208883193338486800929441289451221625718131801098051302305471132, 3036342156106828144759248010981139574855798606498331531979038953098962363448, 19366094066241768814260448581651334103981841220978983881367080466233114693224, 123537904053024229826136306344581357620861422363929109137147685636175105004260
Implicit equation for the generating function in Maple syntax:
F(x)^5-4*F(x)^4+6*F(x)^3-3*F(x)^2+(x-2)*F(x)+2 = 0
Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{5}-4 F \! \left(x \right)^{4}+6 F \! \left(x \right)^{3}-3 F \! \left(x \right)^{2}+\left(x -2\right) F \! \left(x \right)+2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 23
a(5) = 102
a(6) = 492
a(7) = 2498
a(8) = 13130
a(9) = 70800
a(n+10) = 216/4577975*n*(4*n+5)*(2*n+1)*(4*n-1)/(n+10)/(n+9)/(n+8)/(n+7)*a(n)-36/22889875*(6368*n^4+7792*n^3-18886*n^2-31977*n-12042)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+1)-4/22889875*(470816*n^4+8357744*n^3+38681974*n^2+69859891*n+44181282)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+2)+1/22889875*(43164643*n^4+575126450*n^3+2846628929*n^2+6215661292*n+5058417432)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+3)-1/45779750*(557299991*n^4+8588700937*n^3+49566860404*n^2+126880219526*n+121477172112)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+4)+1/22889875*(691999860*n^4+12983326459*n^3+91058985384*n^2+282856686983*n+328212136590)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+5)-1/45779750*(1295392235*n^4+28657906627*n^3+238994266489*n^2+891923004767*n+1258904957070)/(n+10)/(n+9)/(n+8)/(n+7)*a(n+6)+3/183119000*(2547757467*n^3+54035474921*n^2+385270020154*n+921657568480)/(n+8)/(n+9)/(n+10)*a(n+7)-1/91559500*(2771667903*n^2+43784936273*n+173158009350)/(n+9)/(n+10)*a(n+8)+3/1831190*(6252531*n+53053816)/(n+10)*a(n+9), n >= 10
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) = 102
a \! \left(6\right) = 492
a \! \left(7\right) = 2498
a \! \left(8\right) = 13130
a \! \left(9\right) = 70800
a \! \left(n +10\right) = \frac{216 n \left(4 n +5\right) \left(2 n +1\right) \left(4 n -1\right) a \! \left(n \right)}{4577975 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}-\frac{36 \left(6368 n^{4}+7792 n^{3}-18886 n^{2}-31977 n -12042\right) a \! \left(n +1\right)}{22889875 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}-\frac{4 \left(470816 n^{4}+8357744 n^{3}+38681974 n^{2}+69859891 n +44181282\right) a \! \left(n +2\right)}{22889875 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}+\frac{\left(43164643 n^{4}+575126450 n^{3}+2846628929 n^{2}+6215661292 n +5058417432\right) a \! \left(n +3\right)}{22889875 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}-\frac{\left(557299991 n^{4}+8588700937 n^{3}+49566860404 n^{2}+126880219526 n +121477172112\right) a \! \left(n +4\right)}{45779750 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}+\frac{\left(691999860 n^{4}+12983326459 n^{3}+91058985384 n^{2}+282856686983 n +328212136590\right) a \! \left(n +5\right)}{22889875 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}-\frac{\left(1295392235 n^{4}+28657906627 n^{3}+238994266489 n^{2}+891923004767 n +1258904957070\right) a \! \left(n +6\right)}{45779750 \left(n +10\right) \left(n +9\right) \left(n +8\right) \left(n +7\right)}+\frac{3 \left(2547757467 n^{3}+54035474921 n^{2}+385270020154 n +921657568480\right) a \! \left(n +7\right)}{183119000 \left(n +8\right) \left(n +9\right) \left(n +10\right)}-\frac{\left(2771667903 n^{2}+43784936273 n +173158009350\right) a \! \left(n +8\right)}{91559500 \left(n +9\right) \left(n +10\right)}+\frac{3 \left(6252531 n +53053816\right) a \! \left(n +9\right)}{1831190 \left(n +10\right)}, \quad n \geq 10
Specification 1
Strategy pack name: point_and_row_and_col_placements_expand_verified
Tree: http://permpal.com/tree/24054/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[0,x]*F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[0,x]*F[11,x]*F[7,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[31,x]
F[15,x] = 1/F[11,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[8,x]+F[18,x]
F[18,x] = F[19,x]+F[21,x]
F[19,x] = 1/F[11,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[23,x]
F[23,x] = 1/F[11,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]*F[19,x]*F[27,x]
F[27,x] = 1/F[11,x]*F[28,x]
F[28,x] = -F[1,x]-F[29,x]+F[19,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[19,x]+F[25,x]
F[31,x] = F[32,x]
F[32,x] = F[19,x]^2*F[11,x]*F[4,x]*F[8,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_{3}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{28}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{29}\! \left(x \right)+F_{19}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \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))
Eq(F_3(x), F_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_0(x)*F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_0(x)*F_11(x)*F_7(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_31(x))
Eq(F_15(x), F_16(x)/F_11(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) - F_8(x))
Eq(F_18(x), F_19(x) + F_21(x))
Eq(F_19(x), F_20(x)/F_11(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_23(x))
Eq(F_23(x), F_24(x)/F_11(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x)*F_19(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_11(x))
Eq(F_28(x), -F_1(x) + F_19(x) - F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_19(x) + F_25(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_11(x)*F_19(x)**2*F_4(x)*F_8(x))
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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_row_and_col_placements_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": [1, 3, 0, 2], "pos": [[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, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], 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"RowColumnSeparationStrategy", "workable": true}}, "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"}}]}
Specification 2
Strategy pack name: point_and_row_and_col_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24055/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[0,x]*F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[12,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[0,x]*F[7,x]*F[8,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[7,x]
F[14,x] = F[15,x]+F[31,x]
F[15,x] = 1/F[7,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[7,x]*F[9,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[0,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[0,x]*F[19,x]*F[7,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[7,x]
F[25,x] = 1/F[7,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[30,x]+F[28,x]
F[28,x] = 1/F[7,x]*F[29,x]
F[29,x] = F[10,x]
F[30,x] = F[17,x]+F[9,x]
F[31,x] = F[32,x]
F[32,x] = F[20,x]*F[33,x]*F[4,x]*F[7,x]*F[9,x]
F[33,x] = F[0,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[28,x]*F[7,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_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{0}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{12}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{0}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{20}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right) F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right) F_{7}\! \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))
Eq(F_3(x), F_4(x)*F_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_0(x)*F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_12(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_0(x)*F_7(x)*F_8(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_31(x))
Eq(F_15(x), F_16(x)/F_7(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_7(x)*F_9(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_0(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_0(x)*F_19(x)*F_7(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_7(x))
Eq(F_25(x), F_26(x)/F_7(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_30(x))
Eq(F_28(x), F_29(x)/F_7(x))
Eq(F_29(x), F_10(x))
Eq(F_30(x), F_17(x) + F_9(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_20(x)*F_33(x)*F_4(x)*F_7(x)*F_9(x))
Eq(F_33(x), F_0(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_28(x)*F_7(x))
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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_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": [1, 3, 0, 2], "pos": [[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, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 1], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 3], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 2], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 5, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [4, 2, 0, 5, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [0, 2], [2, 1], [2, 3]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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