0123_0231_0321_1203_2103
Counting sequence:
1, 1, 2, 6, 19, 51, 123, 316, 842, 2229, 5808, 15098, 39462, 103350, 270326, 706311, 1845755, 4825462, 12616168, 32980493, 86210949, 225362683, 589133954, 1540083878, 4025963537, 10524333560, 27511920140, 71919698196, 188007184256, 491474177396, 1284774784561, 3358562477837, 8779704090270, 22951246962546, 59997433893679, 156840809424091, 410001535035771, 1071795401858964, 2801807496955502, 7324275907774717, 19146575115711640, 50051546893758054, 130841016210675962, 342034813635140206, 894121867380817114, 2337346615078793895, 6110116974569947311, 15972611507335431818, 41754408208325959956, 109151255826322675473, 285335061849941900941, 745901610608717883539, 1949880288453124114626, 5097231438059802141922, 13324801777343075025921, 34832701744695815965232, 91057047685135696141416, 238034534154175518184152, 622252103383822913539392, 1626644980492016464467224, 4252253834372070532599233, 11115924426522385112911593, 29058419527394245498518890, 75962350321071992751667758, 198575103537943884164142651, 519100206594932561784402467, 1356992995022717507888917883, 3547349750869275733761378220, 9273216811838930370313439618, 24241350889716979892726440261, 63369929214655037625985455232, 165656936650912577999874197346, 433047992962222350470584994302, 1132041724300326300961331049862, 2959298937724556938037914955310, 7735978290226317787686367065959, 20222816743505058073625164276115, 52864977343340533002389797247406, 138195675951495767143834428433872, 361260815977567613270225440327397, 944381047107323743072950858967605, 2468730409419505771863550467859339, 6453570677917236129840470959085922, 16870442530282733157667734400966382, 44101451021750547658786663854382289, 115286719879023057575368863772032680, 301373933794361598874094773277699668, 787829231901102050771072726907075212, 2059484344991128201196421532970703808, 5383750177723766176734844443810581676, 14073797670098601208232182609239065009, 36790670874445549632673320029351166677, 96175424368047849775936884788644785574, 251414612251576373804068584738890349050, 657229304356575174564830919966160088951, 1718079767268258242592960296341298230283, 4491275825849473907986539708730999846523, 11740757867099845083855232937487355860100, 30691812446810703222424457662471094927174, 80232244113462016453249840095492224523789, 209737141025409673337886462610409662127720
Generating function in Maple syntax:
-(x-1)/(x^7+5*x^6-4*x^5-5*x^4-2*x^3-2*x+1)
Generating function in latex syntax:
-\frac{x -1}{x^{7}+5 x^{6}-4 x^{5}-5 x^{4}-2 x^{3}-2 x +1}
Generating function in sympy syntax:
(1 - x)/(x**7 + 5*x**6 - 4*x**5 - 5*x**4 - 2*x**3 - 2*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^7+5*x^6-4*x^5-5*x^4-2*x^3-2*x+1)*F(x)+x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}+5 x^{6}-4 x^{5}-5 x^{4}-2 x^{3}-2 x +1\right) F \! \left(x \right)+x -1 = 0
Explicit closed form in Maple syntax:
-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n+5)-3876744587/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n+5)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n+4)-22463841220/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n+4)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n+3)-2382203227/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n+3)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n+2)+16921221193/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n+2)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n+1)+23834481936/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n+1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n-1)+11177622699/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n-1)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 1)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 2)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 3)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 4)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 5)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 6)^(-n)+39318617202/204764767241*RootOf(_Z^7+5*_Z^6-4*_Z^5-5*_Z^4-2*_Z^3-2*_Z+1,index = 7)^(-n)
Explicit closed form in latex syntax:
-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{204764767241}-\frac{3876744587 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{204764767241}-\frac{22463841220 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{204764767241}-\frac{2382203227 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{204764767241}+\frac{16921221193 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{204764767241}+\frac{23834481936 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{204764767241}+\frac{11177622699 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{204764767241}+\frac{39318617202 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+5 \textit{\_Z}^{6}-4 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}-2 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{204764767241}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 123
a(n+4) = 1/2*a(n)+5/2*a(n+1)-2*a(n+2)-5/2*a(n+3)-a(n+6)+1/2*a(n+7), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 51
a \! \left(6\right) = 123
a \! \left(n +4\right) = \frac{a \! \left(n \right)}{2}+\frac{5 a \! \left(n +1\right)}{2}-2 a \! \left(n +2\right)-\frac{5 a \! \left(n +3\right)}{2}-a \! \left(n +6\right)+\frac{a \! \left(n +7\right)}{2}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17091/
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[20,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[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[89,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[39,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[33,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[15,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[4,x]
F[39,x] = F[40,x]+F[55,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[49,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[2,x]*F[4,x]
F[49,x] = F[50,x]+F[52,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[46,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[44,x]
F[55,x] = 2*F[22,x]+F[56,x]+F[62,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[44,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[47,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[86,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]+F[51,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[77,x]
F[68,x] = F[15,x]+F[69,x]
F[69,x] = F[22,x]+F[70,x]+F[75,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = x^2
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[15,x]
F[77,x] = F[50,x]+F[78,x]
F[78,x] = 2*F[22,x]+F[79,x]+F[84,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[47,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[47,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[65,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[47,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[43,x]+F[91,x]
F[91,x] = F[65,x]+F[92,x]
F[92,x] = F[53,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_{20}\! \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_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{89}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{55}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{44}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{86}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{77}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
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_{4}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = x^{2}
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right)
F_{77}\! \left(x \right) = F_{50}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{79}\! \left(x \right)+F_{84}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{47}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{65}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{47}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{43}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{65}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{53}\! \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_20(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))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_89(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_39(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_33(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_15(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_4(x))
Eq(F_39(x), F_40(x) + F_55(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_49(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_2(x)*F_4(x))
Eq(F_49(x), F_50(x) + F_52(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_46(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_44(x))
Eq(F_55(x), 2*F_22(x) + F_56(x) + F_62(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_44(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_86(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x) + F_51(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_77(x))
Eq(F_68(x), F_15(x) + F_69(x))
Eq(F_69(x), F_22(x) + F_70(x) + F_75(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), x**2)
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_15(x))
Eq(F_77(x), F_50(x) + F_78(x))
Eq(F_78(x), 2*F_22(x) + F_79(x) + F_84(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_47(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_47(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_65(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_47(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_43(x) + F_91(x))
Eq(F_91(x), F_65(x) + F_92(x))
Eq(F_92(x), F_53(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:
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