01324_01342_01432_03124_03142_03214_10324_10342_10432_13024_13042_13402_14032_14302_30124_30142_30214_31024_31042_31402
Counting sequence:
1, 1, 2, 6, 24, 100, 402, 1560, 5922, 22218, 82874, 308288, 1145482, 4254332, 15798942, 58672434, 217904362, 809325720, 3006082846, 11165874556, 41475709714, 154063818402, 572283061890, 2125803214608, 7896529819618, 29332565446788, 108959245568422, 404741979133626, 1503462033614410, 5584788062749320, 20745357823108902, 77061092276614884, 286252564963265706, 1063319087053456314, 3949824778901240370, 14672092235103778496, 54501225256282272906, 202451259314098867324, 752029191412260681902, 2793501538911142955586, 10376792463498694035594, 38545825128699934744664, 143183034640052862083502, 531870347558643865673324, 1975695425929214193600578, 7338954754562256233404754, 27261417009252418685335010, 101265763614541636630654864, 376163677660977941465492274, 1397304551320880544895630036, 5190453318842780857838729974, 19280553856088269155815324362, 71619901800892356102277982922, 266040611294508295204011683528, 988239373110691049219557823222, 3670932245322305181936598696788, 13636112784425633371252176970202, 50652956645145946037415538680042, 188156409194962773055547849757202, 698929276116303754120630540112000, 2596255610438907022037511411858522, 9644099088523311304135411569951500, 35824148768438358997336902881158654, 133073045310208523694290839165332434, 494315594282430482443710267423554314, 1836193845126106520750890757248181464, 6820759603534994517677007073636992126, 25336519721325910677467518866641176860, 94115504562928590250760082378723801586, 349603193199381114291981995559934899458, 1298642484708585450151964234045053440962, 4823961382207060643498764837477542134928, 17919176132796058639029550862558763484034, 66562902941660687059523951686643275649956, 247255789841360259922090330095565712185158, 918460928058640876843862411645592739851482, 3411731943310917657256230714461689487686986, 12673282550637710147290380109165128764496776, 47076409658500939639928165067092321988169670, 174870901637357056163602190874706276488988996, 649578684128477872608721941688417144352379146, 2412936989077344633695908970881822367556073498, 8963140348531012406639004244068691214385588210, 33294646843713943453985361742861157090877027520, 123676910696741539296067994226417939558465819690, 459412538937251859776286747592150081882609095964, 1706542310474550503363253390487616472599200016462, 6339153615999991730016979513913367036408063057250, 23547537216391239059068820674852303189815450504586, 87470117076483099165865227197275729120893336920536, 324918113986368382932187882975379365077958577297998, 1206946833101270952447559936829038651580064664713036, 4483347019533366088126470082249382392679460279031714, 16653923724138193389854925765250129420296253979298994, 61862972953246950220000523347064379098241719422151586, 229797343016965484449287060538611472618860846712576016, 853609458723649460154151014815379432750318165889667538, 3170833476384829590554213535784933944638064026542944756, 11778436651810439930920887289963490280467798724389959318, 43752398539353098767895574908993224254597661433725531370, 162523468481884494705241874346649611166581532050869354442
Generating function in Maple syntax:
(4*x^3-5*x^2+4*x-1)*(x^2-3*x+1)^2/(x-1)/(2*x^7+10*x^6-52*x^5+87*x^4-78*x^3+39*x^2-10*x+1)
Generating function in latex syntax:
\frac{\left(4 x^{3}-5 x^{2}+4 x -1\right) \left(x^{2}-3 x +1\right)^{2}}{\left(x -1\right) \left(2 x^{7}+10 x^{6}-52 x^{5}+87 x^{4}-78 x^{3}+39 x^{2}-10 x +1\right)}
Generating function in sympy syntax:
(x**2 - 3*x + 1)**2*(4*x**3 - 5*x**2 + 4*x - 1)/((x - 1)*(2*x**7 + 10*x**6 - 52*x**5 + 87*x**4 - 78*x**3 + 39*x**2 - 10*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x^7+10*x^6-52*x^5+87*x^4-78*x^3+39*x^2-10*x+1)*F(x)-(4*x^3-5*x^2+4*x-1)*(x^2-3*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x^{7}+10 x^{6}-52 x^{5}+87 x^{4}-78 x^{3}+39 x^{2}-10 x +1\right) F \! \left(x \right)-\left(4 x^{3}-5 x^{2}+4 x -1\right) \left(x^{2}-3 x +1\right)^{2} = 0
Explicit closed form in Maple syntax:
2-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+6)-125490028/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+6)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+5)-619261352/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+5)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+4)+3308762214/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+4)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+3)-5645792806/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+3)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+2)+5118171406/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+2)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n+1)-2580302448/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n+1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n-1)-61778111/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n-1)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 1)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 2)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 3)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 4)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 5)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 6)^(-n)+650608791/22458833*RootOf(2*_Z^7+10*_Z^6-52*_Z^5+87*_Z^4-78*_Z^3+39*_Z^2-10*_Z+1,index = 7)^(-n)
Explicit closed form in latex syntax:
2-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{22458833}-\frac{125490028 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{22458833}-\frac{619261352 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{22458833}+\frac{3308762214 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{22458833}-\frac{5645792806 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{22458833}+\frac{5118171406 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{22458833}-\frac{2580302448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{22458833}-\frac{61778111 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{22458833}+\frac{650608791 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}+10 \textit{\_Z}^{6}-52 \textit{\_Z}^{5}+87 \textit{\_Z}^{4}-78 \textit{\_Z}^{3}+39 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{22458833}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 402
a(7) = 1560
a(n+7) = -2*a(n)-10*a(n+1)+52*a(n+2)-87*a(n+3)+78*a(n+4)-39*a(n+5)+10*a(n+6)-2, n >= 8
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 402
a(7) = 1560
a{\left(n + 7 \right)} = - 2 a{\left(n \right)} - 10 a{\left(n + 1 \right)} + 52 a{\left(n + 2 \right)} - 87 a{\left(n + 3 \right)} + 78 a{\left(n + 4 \right)} - 39 a{\left(n + 5 \right)} + 10 a{\left(n + 6 \right)} - 2, \quad n \geq 8
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24972/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[22,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[6,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]+F[13,x]+F[16,x]
F[12,x] = 0
F[13,x] = F[14,x]*F[15,x]
F[14,x] = F[6,x]
F[15,x] = x
F[16,x] = F[15,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[15,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]+F[16,x]+F[21,x]
F[21,x] = F[15,x]*F[6,x]
F[22,x] = F[115,x]+F[12,x]+F[23,x]
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[25,x]+F[68,x]
F[25,x] = F[2,x]+F[26,x]
F[26,x] = F[12,x]+F[27,x]+F[65,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[26,x]+F[30,x]
F[30,x] = F[12,x]+F[31,x]+F[33,x]+F[62,x]
F[31,x] = F[15,x]*F[32,x]
F[32,x] = F[26,x]
F[33,x] = F[15,x]*F[34,x]
F[34,x] = F[35,x]+F[42,x]
F[35,x] = F[36,x]
F[36,x] = F[12,x]+F[37,x]+F[38,x]
F[37,x] = F[15,x]*F[2,x]
F[38,x] = F[15,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]+F[41,x]
F[41,x] = F[37,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]+F[33,x]+F[44,x]+F[45,x]
F[44,x] = F[15,x]*F[26,x]
F[45,x] = F[15,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = 2*F[12,x]+F[49,x]+F[58,x]
F[49,x] = F[15,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[15,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[2,x]+F[50,x]
F[54,x] = F[50,x]+F[55,x]
F[55,x] = 2*F[12,x]+F[56,x]+F[58,x]
F[56,x] = F[15,x]*F[57,x]
F[57,x] = F[50,x]
F[58,x] = F[15,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[41,x]
F[61,x] = F[48,x]
F[62,x] = F[15,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]+F[55,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[50,x]+F[6,x]
F[68,x] = F[22,x]+F[69,x]
F[69,x] = F[109,x]+F[12,x]+F[70,x]+F[72,x]
F[70,x] = F[15,x]*F[71,x]
F[71,x] = F[26,x]
F[72,x] = F[15,x]*F[73,x]
F[73,x] = F[108,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]+F[37,x]+F[76,x]
F[76,x] = F[15,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[15,x]+F[75,x]
F[79,x] = F[80,x]+F[85,x]
F[80,x] = F[12,x]+F[21,x]+F[81,x]
F[81,x] = F[15,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[15,x]+F[20,x]
F[84,x] = F[80,x]
F[85,x] = F[12,x]+F[44,x]+F[86,x]+F[99,x]
F[86,x] = F[15,x]*F[87,x]
F[87,x] = F[88,x]+F[98,x]
F[88,x] = F[75,x]+F[89,x]
F[89,x] = F[12,x]+F[44,x]+F[72,x]+F[90,x]
F[90,x] = F[15,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[20,x]+F[93,x]
F[93,x] = 2*F[12,x]+F[49,x]+F[94,x]
F[94,x] = F[15,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[75,x]
F[97,x] = F[93,x]
F[98,x] = F[85,x]
F[99,x] = F[100,x]*F[15,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]+F[80,x]
F[102,x] = F[103,x]+F[107,x]+F[12,x]+F[49,x]
F[103,x] = F[104,x]*F[15,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[75,x]+F[93,x]
F[106,x] = F[102,x]
F[107,x] = 0
F[108,x] = F[89,x]
F[109,x] = F[110,x]*F[15,x]
F[110,x] = F[111,x]
F[111,x] = F[11,x]+F[112,x]
F[112,x] = 2*F[12,x]+F[113,x]+F[94,x]
F[113,x] = F[114,x]*F[15,x]
F[114,x] = F[50,x]
F[115,x] = F[116,x]*F[15,x]
F[116,x] = F[117,x]+F[122,x]
F[117,x] = F[118,x]+F[6,x]
F[118,x] = F[119,x]+F[12,x]+F[76,x]
F[119,x] = F[120,x]*F[15,x]
F[120,x] = F[121,x]+F[53,x]
F[121,x] = F[112,x]+F[118,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[12,x]+F[13,x]+F[81,x]
F[124,x] = F[12,x]+F[125,x]+F[86,x]+F[99,x]
F[125,x] = F[126,x]*F[15,x]
F[126,x] = F[26,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_{15}\! \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_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{6}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{115}\! \left(x \right)+F_{12}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{68}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right)+F_{27}\! \left(x \right)+F_{65}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)+F_{62}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right)+F_{33}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{49}\! \left(x \right)+F_{58}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{50}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \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_{41}\! \left(x \right)
F_{61}\! \left(x \right) = F_{48}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{50}\! \left(x \right)+F_{6}\! \left(x \right)
F_{68}\! \left(x \right) = F_{22}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{109}\! \left(x \right)+F_{12}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{26}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{108}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right)+F_{37}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right)+F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{85}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{15}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right)+F_{44}\! \left(x \right)+F_{86}\! \left(x \right)+F_{99}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{98}\! \left(x \right)
F_{88}\! \left(x \right) = F_{75}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right)+F_{44}\! \left(x \right)+F_{72}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{15}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{20}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{49}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{15}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{75}\! \left(x \right)
F_{97}\! \left(x \right) = F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{85}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{15}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{80}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{107}\! \left(x \right)+F_{12}\! \left(x \right)+F_{49}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{15}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{75}\! \left(x \right)+F_{93}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right)
F_{107}\! \left(x \right) = 0
F_{108}\! \left(x \right) = F_{89}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{15}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{11}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{113}\! \left(x \right)+F_{94}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{15}\! \left(x \right)
F_{114}\! \left(x \right) = F_{50}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{6}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{12}\! \left(x \right)+F_{76}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{15}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{53}\! \left(x \right)
F_{121}\! \left(x \right) = F_{112}\! \left(x \right)+F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{81}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right)+F_{125}\! \left(x \right)+F_{86}\! \left(x \right)+F_{99}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{15}\! \left(x \right)
F_{126}\! \left(x \right) = F_{26}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_22(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x) + F_13(x) + F_16(x))
Eq(F_12(x), 0)
Eq(F_13(x), F_14(x)*F_15(x))
Eq(F_14(x), F_6(x))
Eq(F_15(x), x)
Eq(F_16(x), F_15(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_15(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x) + F_16(x) + F_21(x))
Eq(F_21(x), F_15(x)*F_6(x))
Eq(F_22(x), F_115(x) + F_12(x) + F_23(x))
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_68(x))
Eq(F_25(x), F_2(x) + F_26(x))
Eq(F_26(x), F_12(x) + F_27(x) + F_65(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_26(x) + F_30(x))
Eq(F_30(x), F_12(x) + F_31(x) + F_33(x) + F_62(x))
Eq(F_31(x), F_15(x)*F_32(x))
Eq(F_32(x), F_26(x))
Eq(F_33(x), F_15(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_42(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_12(x) + F_37(x) + F_38(x))
Eq(F_37(x), F_15(x)*F_2(x))
Eq(F_38(x), F_15(x)*F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x) + F_41(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x) + F_33(x) + F_44(x) + F_45(x))
Eq(F_44(x), F_15(x)*F_26(x))
Eq(F_45(x), F_15(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), 2*F_12(x) + F_49(x) + F_58(x))
Eq(F_49(x), F_15(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_15(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_2(x) + F_50(x))
Eq(F_54(x), F_50(x) + F_55(x))
Eq(F_55(x), 2*F_12(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_15(x)*F_57(x))
Eq(F_57(x), F_50(x))
Eq(F_58(x), F_15(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_41(x))
Eq(F_61(x), F_48(x))
Eq(F_62(x), F_15(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x) + F_55(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_50(x) + F_6(x))
Eq(F_68(x), F_22(x) + F_69(x))
Eq(F_69(x), F_109(x) + F_12(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_15(x)*F_71(x))
Eq(F_71(x), F_26(x))
Eq(F_72(x), F_15(x)*F_73(x))
Eq(F_73(x), F_108(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x) + F_37(x) + F_76(x))
Eq(F_76(x), F_15(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_15(x) + F_75(x))
Eq(F_79(x), F_80(x) + F_85(x))
Eq(F_80(x), F_12(x) + F_21(x) + F_81(x))
Eq(F_81(x), F_15(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_15(x) + F_20(x))
Eq(F_84(x), F_80(x))
Eq(F_85(x), F_12(x) + F_44(x) + F_86(x) + F_99(x))
Eq(F_86(x), F_15(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_98(x))
Eq(F_88(x), F_75(x) + F_89(x))
Eq(F_89(x), F_12(x) + F_44(x) + F_72(x) + F_90(x))
Eq(F_90(x), F_15(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_20(x) + F_93(x))
Eq(F_93(x), 2*F_12(x) + F_49(x) + F_94(x))
Eq(F_94(x), F_15(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_75(x))
Eq(F_97(x), F_93(x))
Eq(F_98(x), F_85(x))
Eq(F_99(x), F_100(x)*F_15(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) + F_80(x))
Eq(F_102(x), F_103(x) + F_107(x) + F_12(x) + F_49(x))
Eq(F_103(x), F_104(x)*F_15(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_75(x) + F_93(x))
Eq(F_106(x), F_102(x))
Eq(F_107(x), 0)
Eq(F_108(x), F_89(x))
Eq(F_109(x), F_110(x)*F_15(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_11(x) + F_112(x))
Eq(F_112(x), F_113(x) + 2*F_12(x) + F_94(x))
Eq(F_113(x), F_114(x)*F_15(x))
Eq(F_114(x), F_50(x))
Eq(F_115(x), F_116(x)*F_15(x))
Eq(F_116(x), F_117(x) + F_122(x))
Eq(F_117(x), F_118(x) + F_6(x))
Eq(F_118(x), F_119(x) + F_12(x) + F_76(x))
Eq(F_119(x), F_120(x)*F_15(x))
Eq(F_120(x), F_121(x) + F_53(x))
Eq(F_121(x), F_112(x) + F_118(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_12(x) + F_13(x) + F_81(x))
Eq(F_124(x), F_12(x) + F_125(x) + F_86(x) + F_99(x))
Eq(F_125(x), F_126(x)*F_15(x))
Eq(F_126(x), F_26(x))
Pack JSON:
{"name": "regular_insertion_encoding_left", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}], "inferral_strats": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "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": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 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