0123_0132_1032_1302_2031

Counting sequence:
1, 1, 2, 6, 19, 57, 167, 488, 1428, 4182, 12250, 35885, 105125, 307974, 902265, 2643400, 7744579, 22690136, 66478236, 194770909, 570650600, 1671928094, 4898529404, 14352065869, 42049760782, 123200631341, 360962882981, 1057577760027, 3098576186001, 9078458744781, 26598804918004, 77931343431095, 228329607098179, 668978738912486, 1960028632916346, 5742652355701775, 16825293299508777, 49296123189089029, 144431822893460746, 423168197423300456, 1239832887880178868, 3632564081949228518, 10642984201613973767, 31182688133609797205, 91361597640524499814, 267678703462275601515, 784267024421787842376, 2297809866415199472611, 6732311852096708465764, 19724879567149033381206, 57791570346632404703373, 169322483927544724544130, 496094904388050509860068, 1453499549878457800158426, 4258582224672907177988207, 12477143571397807778705508, 36556558847767099813481661, 107106405176930236188361171, 313809132796410619778687017, 919423741880421684464965753, 2693803107655588277202574377, 7892525342014611005731144030, 23124168242836464271183026501, 67751085204307863819667001385, 198502687671345647535581498478, 581589459326909104190320440550, 1703988511029211740567260204975, 4992485333350666586810078325785, 14627393108815818510765952827983, 42856536348858260871033892224924, 125564596107995065928797018945180, 367889454887922117008074539768710, 1077872706262994172341947052394978, 3158039882553118499509039627298041, 9252684330762859457769415771509925, 27109273634484347700199475045112282, 79426973915662966164257019606660437, 232711664298323315349724532759159372, 681817725524815349451747408572897719, 1997645507978887106835250740600674492, 5852865694385659989230335798152118996, 17148206075448861874508470230860587969, 50242220983840285769847510139846893548, 147203780866796729642224126948609529238, 431289713654367768174374216038524538804, 1263627985699539396557944513625828158713, 3702280939449217250690495919412020110354, 10847246428323530797535375390794519178873, 31781152484414689935357672193194683888133, 93115027847092322830117896292913736833595, 272816047662736686799412484113214916317721, 799318838034808015646069962879102756482533, 2341909907100318418211643376647902879282552, 6861519774085177465572912725528746968162075, 20103443547260745095133516156667905954444699, 58900718173880568525500438708569200581255482, 172572156269796072549713702157326219125648810, 505616061109647395600512453876189347502666811, 1481395416143262577634014692141216911277954153, 4340313822614835849690980478691440368889799045, 12716607513087913402251215005251309061861203950

Generating function in Maple syntax:
-(x-1)*(2*x-1)*(x^3+2*x-1)/(x^6-2*x^5+7*x^4-11*x^3+12*x^2-6*x+1)

Generating function in latex syntax:
-\frac{\left(x -1\right) \left(2 x -1\right) \left(x^{3}+2 x -1\right)}{x^{6}-2 x^{5}+7 x^{4}-11 x^{3}+12 x^{2}-6 x +1}

Generating function in sympy syntax:
(1 - x)*(2*x - 1)*(x**3 + 2*x - 1)/(x**6 - 2*x**5 + 7*x**4 - 11*x**3 + 12*x**2 - 6*x + 1)

Implicit equation for the generating function in Maple syntax:
(x^6-2*x^5+7*x^4-11*x^3+12*x^2-6*x+1)*F(x)+(x-1)*(2*x-1)*(x^3+2*x-1) = 0

Implicit equation for the generating function in latex syntax:
\left(x^{6}-2 x^{5}+7 x^{4}-11 x^{3}+12 x^{2}-6 x +1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x -1\right) \left(x^{3}+2 x -1\right) = 0

Explicit closed form in Maple syntax:
-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+4)-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+4)-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+4)-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+4)-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+4)-68231/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n+4)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+3)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+3)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+3)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+3)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+3)+87753/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n+3)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+2)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+2)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+2)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+2)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+2)-375095/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n+2)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+1)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+1)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+1)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+1)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n+1)+438475/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n+1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n-1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n-1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n-1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n-1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n-1)+100514/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n-1)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n)-338900/244129*RootOf(_Z^6-2*_Z^5+7*_Z^4-11*_Z^3+12*_Z^2-6*_Z+1,index = 6)^(-n)

Explicit closed form in latex syntax:
-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{244129}-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{244129}-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{244129}-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{244129}-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{244129}-\frac{68231 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{244129}+\frac{87753 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{244129}-\frac{375095 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{244129}+\frac{438475 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{244129}+\frac{100514 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{244129}-\frac{338900 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{5}+7 \textit{\_Z}^{4}-11 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{244129}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 57
a(n+6) = -a(n)+2*a(n+1)-7*a(n+2)+11*a(n+3)-12*a(n+4)+6*a(n+5), n >= 6

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) = 19
a \! \left(5\right) = 57
a \! \left(n +6\right) = -a \! \left(n \right)+2 a \! \left(n +1\right)-7 a \! \left(n +2\right)+11 a \! \left(n +3\right)-12 a \! \left(n +4\right)+6 a \! \left(n +5\right), \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16362/
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[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]+F[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[12,x]
F[18,x] = F[4,x]*F[7,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]+F[63,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[31,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]
F[25,x] = F[10,x]*F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[16,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[27,x]
F[31,x] = F[32,x]+F[57,x]
F[32,x] = F[13,x]+F[21,x]+F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[13,x]+F[36,x]+F[56,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[30,x]+F[4,x]
F[39,x] = F[35,x]+F[40,x]
F[40,x] = 2*F[13,x]+F[41,x]+F[49,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[45,x]
F[43,x] = F[44,x]
F[44,x] = F[16,x]*F[4,x]
F[45,x] = F[46,x]
F[46,x] = 2*F[13,x]+F[41,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[35,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[48,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[35,x]
F[55,x] = F[52,x]
F[56,x] = F[2,x]*F[4,x]
F[57,x] = 2*F[13,x]+F[49,x]+F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[44,x]
F[61,x] = F[62,x]
F[62,x] = 2*F[13,x]+F[47,x]+F[58,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[34,x]+F[65,x]
F[65,x] = F[66,x]+F[78,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[2,x]+F[70,x]
F[70,x] = F[56,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = 2*F[13,x]+F[73,x]+F[77,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[70,x]
F[76,x] = F[72,x]
F[77,x] = F[4,x]*F[66,x]
F[78,x] = 2*F[13,x]+F[77,x]+F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[54,x]+F[81,x]
F[81,x] = F[78,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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)+F_{63}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{57}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)+F_{56}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{30}\! \left(x \right)+F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{41}\! \left(x \right)+F_{49}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{35}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{35}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{49}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{44}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{47}\! \left(x \right)+F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{78}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{2}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{56}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{54}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_12(x))
Eq(F_18(x), F_4(x)*F_7(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x) + F_63(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_31(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_10(x)*F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_16(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_27(x))
Eq(F_31(x), F_32(x) + F_57(x))
Eq(F_32(x), F_13(x) + F_21(x) + F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_13(x) + F_36(x) + F_56(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_30(x) + F_4(x))
Eq(F_39(x), F_35(x) + F_40(x))
Eq(F_40(x), 2*F_13(x) + F_41(x) + F_49(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_45(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_16(x)*F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), 2*F_13(x) + F_41(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_35(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_48(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_35(x))
Eq(F_55(x), F_52(x))
Eq(F_56(x), F_2(x)*F_4(x))
Eq(F_57(x), 2*F_13(x) + F_49(x) + F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_44(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), 2*F_13(x) + F_47(x) + F_58(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_34(x) + F_65(x))
Eq(F_65(x), F_66(x) + F_78(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_2(x) + F_70(x))
Eq(F_70(x), F_56(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), 2*F_13(x) + F_73(x) + F_77(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_70(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_4(x)*F_66(x))
Eq(F_78(x), 2*F_13(x) + F_77(x) + F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_54(x) + F_81(x))
Eq(F_81(x), F_78(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"}]], "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_placements", "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": 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