0123_0321_1302
Counting sequence:
1, 1, 2, 6, 21, 71, 229, 726, 2299, 7296, 23180, 73648, 233935, 742924, 2359143, 7491146, 23786672, 75528789, 239820410, 761475614, 2417816525, 7676955811, 24375507011, 77395827653, 245742882637, 780268393400, 2477461176578, 7866282679471, 24976532154203, 79303921031262, 251800817939396, 799502049521409, 2538528277121914, 8060173966564277, 25592152565525694, 81258576561467493, 258007066146805579, 819207627767795468, 2601095948351343796, 8258834369814562932, 26222925399373149465, 83261364107174781189, 264366184972164043956, 839398687051454700528, 2665205293202252576418, 8462390235422136980630, 26869242930652402555993, 85313510189250782534080, 270882028160480048673460, 860087376704558252308223, 2730894701880115261504644, 8670963060913543656845335, 27531490082957373773354165, 87416235181055577548671607, 277558466691907758667467891, 881285979342287358964063902, 2798203155678234038963948241, 8884676579414419044784250538, 28210059645055962788736954427, 89570786067847529660453812590, 284399459545711466442272397969, 903007064475083217304534483552, 2867170562820891920793658146282, 9103657501376787675161922995260, 28905353932213383546227315550300, 91778440239000563331136279500012, 291409062572174525416903292352717, 925263509905497551752368339441208, 2937837811926583955125091916751413, 9328035653396642003873535653816917, 29617785160841314398886185626228216, 94040506536263262182651708488567977, 298591431518970060984582601591824412, 948068510691904326544970673027850823, 3010246799089605988130061206326212947, 9557944061253567240440638187048810189, 30347775705859283210847357978545722680, 96358326057450315709323528674402330724, 305950824554211084155776640503656703245, 971435587098019257224109909962800264184, 3084440452989405962778579337822541243280, 9793519029355403545853323356336423721900, 31095758352341848103751902928874308674611, 98733272954173332162554864995131803059611, 313491604796611912574480694358051782621911, 995378592620645621693209885953317222773688, 3160462760367243792584774586875363825475592, 10034900221603340657563042887158209500009788, 31862176552219076848443212903696486387457516, 101166755246777566816760364589021711441808208, 321218242902762031353360381384087611357934004, 1019911722204062951282507910312609364218581388, 3238358792106801681240617143295177654967279757, 10282230744198860402041121726944129797347418823, 32647484687194427544211614079309319797683464959, 103660215659130389536545629994664652741218136619, 329135319717668399688957983257472792851337007832, 1045049520655807044015272856368441881640047555604, 3318174729955319456251995279354014209503939653004, 10535657230486741882760955090007235511040808440153, 33452148338132339504366890930858079143540656748250
Generating function in Maple syntax:
(x^3-2*x^2+3*x-1)^2/(x^8-x^7+4*x^6-7*x^5+19*x^4-24*x^3+18*x^2-7*x+1)
Generating function in latex syntax:
\frac{\left(x^{3}-2 x^{2}+3 x -1\right)^{2}}{x^{8}-x^{7}+4 x^{6}-7 x^{5}+19 x^{4}-24 x^{3}+18 x^{2}-7 x +1}
Generating function in sympy syntax:
(x**3 - 2*x**2 + 3*x - 1)**2/(x**8 - x**7 + 4*x**6 - 7*x**5 + 19*x**4 - 24*x**3 + 18*x**2 - 7*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^8-x^7+4*x^6-7*x^5+19*x^4-24*x^3+18*x^2-7*x+1)*F(x)-(x^3-2*x^2+3*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{8}-x^{7}+4 x^{6}-7 x^{5}+19 x^{4}-24 x^{3}+18 x^{2}-7 x +1\right) F \! \left(x \right)-\left(x^{3}-2 x^{2}+3 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+6)-10077483386/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+6)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+5)+5195715820/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+5)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+4)-36749487802/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+4)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+3)+53523980461/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+3)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+2)-161922533903/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+2)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n+1)+159607824744/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n+1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n-1)+20215660086/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n-1)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 1)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 2)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 3)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 4)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 5)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 6)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 7)^(-n)-86988332261/57067572007*RootOf(_Z^8-_Z^7+4*_Z^6-7*_Z^5+19*_Z^4-24*_Z^3+18*_Z^2-7*_Z+1,index = 8)^(-n)
Explicit closed form in latex syntax:
-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{57067572007}-\frac{10077483386 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{57067572007}+\frac{5195715820 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{57067572007}-\frac{36749487802 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{57067572007}+\frac{53523980461 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{57067572007}-\frac{161922533903 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{57067572007}+\frac{159607824744 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{57067572007}+\frac{20215660086 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{57067572007}-\frac{86988332261 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+19 \textit{\_Z}^{4}-24 \textit{\_Z}^{3}+18 \textit{\_Z}^{2}-7 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{57067572007}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 71
a(6) = 229
a(7) = 726
a(n+8) = -a(n)+a(n+1)-4*a(n+2)+7*a(n+3)-19*a(n+4)+24*a(n+5)-18*a(n+6)+7*a(n+7), n >= 8
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) = 21
a \! \left(5\right) = 71
a \! \left(6\right) = 229
a \! \left(7\right) = 726
a \! \left(n +8\right) = -a \! \left(n \right)+a \! \left(n +1\right)-4 a \! \left(n +2\right)+7 a \! \left(n +3\right)-19 a \! \left(n +4\right)+24 a \! \left(n +5\right)-18 a \! \left(n +6\right)+7 a \! \left(n +7\right), \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14652/
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[26,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[24,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[4,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[15,x]
F[26,x] = F[2,x]+F[27,x]
F[27,x] = F[150,x]+F[18,x]+F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[42,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[18,x]+F[32,x]+F[40,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[22,x]
F[36,x] = F[17,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[35,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[14,x]
F[42,x] = F[27,x]+F[43,x]
F[43,x] = F[136,x]+F[147,x]+F[18,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[55,x]
F[46,x] = F[31,x]+F[47,x]
F[47,x] = F[18,x]+F[48,x]+F[52,x]+F[54,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[35,x]
F[51,x] = F[37,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[36,x]
F[54,x] = 0
F[55,x] = F[43,x]+F[56,x]
F[56,x] = F[104,x]+F[146,x]+F[18,x]+F[57,x]+F[94,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[63,x]
F[59,x] = F[47,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[51,x]
F[63,x] = F[56,x]+F[64,x]
F[64,x] = F[102,x]+F[103,x]+F[18,x]+F[65,x]+F[69,x]+F[70,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[60,x]
F[68,x] = F[64,x]
F[69,x] = 0
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = 2*F[18,x]+F[77,x]+F[98,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = F[35,x]+F[80,x]
F[80,x] = F[48,x]
F[81,x] = F[76,x]+F[82,x]
F[82,x] = 2*F[18,x]+F[83,x]+F[94,x]+F[97,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = F[80,x]+F[86,x]
F[86,x] = F[61,x]
F[87,x] = F[82,x]+F[88,x]
F[88,x] = 2*F[18,x]+F[69,x]+F[70,x]+F[89,x]+F[93,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[86,x]
F[92,x] = F[88,x]
F[93,x] = 0
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[72,x]+F[96,x]
F[96,x] = F[76,x]
F[97,x] = 0
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]
F[101,x] = F[2,x]*F[4,x]
F[102,x] = 0
F[103,x] = 0
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]+F[73,x]
F[107,x] = 2*F[18,x]+F[108,x]+F[139,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[145,x]
F[110,x] = F[111,x]+F[144,x]+F[18,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[115,x]
F[113,x] = F[11,x]+F[114,x]
F[114,x] = F[18,x]+F[24,x]+F[32,x]
F[115,x] = F[110,x]+F[116,x]
F[116,x] = F[117,x]+F[136,x]+F[139,x]+F[18,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[122,x]
F[119,x] = F[114,x]+F[120,x]
F[120,x] = F[121,x]+F[18,x]+F[48,x]+F[52,x]
F[121,x] = 0
F[122,x] = F[116,x]+F[123,x]
F[123,x] = F[104,x]+F[124,x]+F[135,x]+F[18,x]+F[94,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[120,x]+F[127,x]
F[127,x] = F[61,x]
F[128,x] = F[123,x]+F[129,x]
F[129,x] = F[102,x]+F[130,x]+F[134,x]+F[18,x]+F[69,x]+F[70,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[127,x]
F[133,x] = F[129,x]
F[134,x] = 0
F[135,x] = 0
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[106,x]+F[138,x]
F[138,x] = F[110,x]+F[76,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[100,x]+F[2,x]
F[144,x] = F[143,x]*F[4,x]
F[145,x] = F[98,x]
F[146,x] = 0
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]
F[149,x] = F[107,x]+F[141,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[149,x]+F[152,x]
F[152,x] = F[110,x]+F[2,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_{26}\! \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_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{150}\! \left(x \right)+F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{42}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)+F_{40}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{136}\! \left(x \right)+F_{147}\! \left(x \right)+F_{18}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{46}\! \left(x \right) = F_{31}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{35}\! \left(x \right)
F_{51}\! \left(x \right) = F_{37}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{36}\! \left(x \right)
F_{54}\! \left(x \right) = 0
F_{55}\! \left(x \right) = F_{43}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{104}\! \left(x \right)+F_{146}\! \left(x \right)+F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{94}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{47}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{51}\! \left(x \right)
F_{63}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)+F_{18}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = 0
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{77}\! \left(x \right)+F_{98}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{35}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{48}\! \left(x \right)
F_{81}\! \left(x \right) = F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{83}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{61}\! \left(x \right)
F_{87}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)+F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = 0
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{72}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{76}\! \left(x \right)
F_{97}\! \left(x \right) = 0
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = 0
F_{103}\! \left(x \right) = 0
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{73}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{108}\! \left(x \right)+F_{139}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{145}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{144}\! \left(x \right)+F_{18}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{115}\! \left(x \right)
F_{113}\! \left(x \right) = F_{11}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{136}\! \left(x \right)+F_{139}\! \left(x \right)+F_{18}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{122}\! \left(x \right)
F_{119}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{121}\! \left(x \right) = 0
F_{122}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{104}\! \left(x \right)+F_{124}\! \left(x \right)+F_{135}\! \left(x \right)+F_{18}\! \left(x \right)+F_{94}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{120}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{61}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{102}\! \left(x \right)+F_{130}\! \left(x \right)+F_{134}\! \left(x \right)+F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)
F_{133}\! \left(x \right) = F_{129}\! \left(x \right)
F_{134}\! \left(x \right) = 0
F_{135}\! \left(x \right) = 0
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{106}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{110}\! \left(x \right)+F_{76}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{100}\! \left(x \right)+F_{2}\! \left(x \right)
F_{144}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{98}\! \left(x \right)
F_{146}\! \left(x \right) = 0
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{107}\! \left(x \right)+F_{141}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{149}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{110}\! \left(x \right)+F_{2}\! \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_26(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_24(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_15(x))
Eq(F_26(x), F_2(x) + F_27(x))
Eq(F_27(x), F_150(x) + F_18(x) + F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_42(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_18(x) + F_32(x) + F_40(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_22(x))
Eq(F_36(x), F_17(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_14(x))
Eq(F_42(x), F_27(x) + F_43(x))
Eq(F_43(x), F_136(x) + F_147(x) + F_18(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_55(x))
Eq(F_46(x), F_31(x) + F_47(x))
Eq(F_47(x), F_18(x) + F_48(x) + F_52(x) + F_54(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_35(x))
Eq(F_51(x), F_37(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_36(x))
Eq(F_54(x), 0)
Eq(F_55(x), F_43(x) + F_56(x))
Eq(F_56(x), F_104(x) + F_146(x) + F_18(x) + F_57(x) + F_94(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_63(x))
Eq(F_59(x), F_47(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_51(x))
Eq(F_63(x), F_56(x) + F_64(x))
Eq(F_64(x), F_102(x) + F_103(x) + F_18(x) + F_65(x) + F_69(x) + F_70(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_60(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), 0)
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), 2*F_18(x) + F_77(x) + F_98(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_35(x) + F_80(x))
Eq(F_80(x), F_48(x))
Eq(F_81(x), F_76(x) + F_82(x))
Eq(F_82(x), 2*F_18(x) + F_83(x) + F_94(x) + F_97(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), F_80(x) + F_86(x))
Eq(F_86(x), F_61(x))
Eq(F_87(x), F_82(x) + F_88(x))
Eq(F_88(x), 2*F_18(x) + F_69(x) + F_70(x) + F_89(x) + F_93(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_86(x))
Eq(F_92(x), F_88(x))
Eq(F_93(x), 0)
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_72(x) + F_96(x))
Eq(F_96(x), F_76(x))
Eq(F_97(x), 0)
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_2(x)*F_4(x))
Eq(F_102(x), 0)
Eq(F_103(x), 0)
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) + F_73(x))
Eq(F_107(x), F_108(x) + F_139(x) + 2*F_18(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_145(x))
Eq(F_110(x), F_111(x) + F_144(x) + F_18(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_115(x))
Eq(F_113(x), F_11(x) + F_114(x))
Eq(F_114(x), F_18(x) + F_24(x) + F_32(x))
Eq(F_115(x), F_110(x) + F_116(x))
Eq(F_116(x), F_117(x) + F_136(x) + F_139(x) + F_18(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_122(x))
Eq(F_119(x), F_114(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_18(x) + F_48(x) + F_52(x))
Eq(F_121(x), 0)
Eq(F_122(x), F_116(x) + F_123(x))
Eq(F_123(x), F_104(x) + F_124(x) + F_135(x) + F_18(x) + F_94(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_120(x) + F_127(x))
Eq(F_127(x), F_61(x))
Eq(F_128(x), F_123(x) + F_129(x))
Eq(F_129(x), F_102(x) + F_130(x) + F_134(x) + F_18(x) + F_69(x) + F_70(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_127(x))
Eq(F_133(x), F_129(x))
Eq(F_134(x), 0)
Eq(F_135(x), 0)
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_106(x) + F_138(x))
Eq(F_138(x), F_110(x) + F_76(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_100(x) + F_2(x))
Eq(F_144(x), F_143(x)*F_4(x))
Eq(F_145(x), F_98(x))
Eq(F_146(x), 0)
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_107(x) + F_141(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_149(x) + F_152(x))
Eq(F_152(x), F_110(x) + F_2(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}], "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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}], "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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [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": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": 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