0123_0231_2103
Counting sequence:
1, 1, 2, 6, 21, 72, 233, 739, 2343, 7458, 23801, 76016, 242777, 775265, 2475513, 7904587, 25240597, 80598107, 257366469, 821825201, 2624260190, 8379812195, 26758495711, 85445488885, 272845382481, 871252605664, 2782092566535, 8883805937470, 28367858414881, 90584530704662, 289255434382502, 923653362263309, 2949419206683257, 9418115077601067, 30074019799467648, 96032662530106732, 306652463961136147, 979205732472131768, 3126809594562163790, 9984559849319885775, 31882796943607216238, 101808467903271419728, 325095823780673517259, 1038099254573419445119, 3314868981746749338909, 10585072976150548681463, 33800361500681101144127, 107931654335387886590925, 344648444287762229155240, 1100534879052895701725834, 3514239045862943588225468, 11221703470312385280116865, 35833256398384532555693515, 114423114771239111846066280, 365377041047891318137140080, 1166725642732359266431265427, 3725600058244527123626184852, 11896623581089530537076259119, 37988418085011283894667033645, 121304998747337594339574572399, 387352342183932361522774580102, 1236897395365344322474645371617, 3949673204596501930300162577910, 12612136205929861016655374016097, 40273200195856970444447867119185, 128600787965879176235291288603211, 410649329703536861345986087255573, 1311289570252916349988789057001349, 4187223045744249309049969301592535, 13370682748151564619165961069597279, 42695398644554855673115186771331507, 136335376416695231249442864571053834, 435347495345438311717305181955287081, 1390156001214791501266156691906745865, 4439060126394153144883157303394434981, 14174851447264181735206320522349726033, 45263278223541413697146282530370278670, 144535155318127885789507417688993011779, 461531111813511042351268684620100412070, 1473765788696664403405001612057606936017, 4706043740796235776337482162904594126164, 15027386210310361291468467017524479327186, 47985600804385670663923350606048642842647, 153228103166605355481163090933747844282043, 489289520323980010944155779664972320485375, 1562404217968850910161796607935322831659380, 4989084864745300116420491408606946119485836, 15931195974361400380661737305297197136699007, 50871655234204137740314822798804446642044466, 162443881202174832008911213941079658925122238, 518717435446920687861684781278148683485590917, 1656373732549231877744422049969520472964518416, 5289149263924865196040737189003854016277853682, 16889364632112365483393516221155180640284439365, 53931289030170991879712800821181049913737257007, 172213934615731201407043037620564977918066832837, 549915268282199823686005517251248438807037966801, 1755994966171917989153924810952388613012704378489, 5607260789199887057862457188674662077634216723277, 17905161554443955549861894123621342842201546669436, 57174941980268461465070761723408609824804782708278
Generating function in Maple syntax:
-(2*x^3-2*x^2+3*x-1)*(x-1)^3/(2*x^9-7*x^8+7*x^7-10*x^6+16*x^5-27*x^4+29*x^3-19*x^2+7*x-1)
Generating function in latex syntax:
-\frac{\left(2 x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}{2 x^{9}-7 x^{8}+7 x^{7}-10 x^{6}+16 x^{5}-27 x^{4}+29 x^{3}-19 x^{2}+7 x -1}
Generating function in sympy syntax:
(x - 1)**3*(-2*x**3 + 2*x**2 - 3*x + 1)/(2*x**9 - 7*x**8 + 7*x**7 - 10*x**6 + 16*x**5 - 27*x**4 + 29*x**3 - 19*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^9-7*x^8+7*x^7-10*x^6+16*x^5-27*x^4+29*x^3-19*x^2+7*x-1)*F(x)+(2*x^3-2*x^2+3*x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{9}-7 x^{8}+7 x^{7}-10 x^{6}+16 x^{5}-27 x^{4}+29 x^{3}-19 x^{2}+7 x -1\right) F \! \left(x \right)+\left(2 x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+7)+7773522306412/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+7)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+6)-17197128899924/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+6)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+5)-503978917767/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+5)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+4)-28210749107609/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+4)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+3)+30367576347142/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+3)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+2)-49508038799496/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+2)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+1)+27900764993883/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n+1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n-1)+3662787507320/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n-1)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n)-4589134725087/53865277956337*RootOf(2*_Z^9-7*_Z^8+7*_Z^7-10*_Z^6+16*_Z^5-27*_Z^4+29*_Z^3-19*_Z^2+7*_Z-1,index = 9)^(-n)
Explicit closed form in latex syntax:
\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +7}}{53865277956337}+\frac{7773522306412 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +7}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +6}}{53865277956337}-\frac{17197128899924 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +6}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +5}}{53865277956337}-\frac{503978917767 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +5}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +4}}{53865277956337}-\frac{28210749107609 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +4}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +3}}{53865277956337}+\frac{30367576347142 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +3}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +2}}{53865277956337}-\frac{49508038799496 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +2}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +1}}{53865277956337}+\frac{27900764993883 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{53865277956337}+\frac{3662787507320 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n -1}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{53865277956337}-\frac{4589134725087 \mathit{RootOf}\! \left(2 \textit{\_Z}^{9}-7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}-10 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-27 \textit{\_Z}^{4}+29 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =9\right)^{-n}}{53865277956337}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 72
a(6) = 233
a(7) = 739
a(8) = 2343
a(n+9) = 2*a(n)-7*a(n+1)+7*a(n+2)-10*a(n+3)+16*a(n+4)-27*a(n+5)+29*a(n+6)-19*a(n+7)+7*a(n+8), n >= 9
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) = 72
a \! \left(6\right) = 233
a \! \left(7\right) = 739
a \! \left(8\right) = 2343
a \! \left(n +9\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+7 a \! \left(n +2\right)-10 a \! \left(n +3\right)+16 a \! \left(n +4\right)-27 a \! \left(n +5\right)+29 a \! \left(n +6\right)-19 a \! \left(n +7\right)+7 a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14642/
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[17,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[11,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[71,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[33,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[30,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]+F[27,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[13,x]+F[32,x]
F[32,x] = F[23,x]
F[33,x] = F[34,x]+F[44,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[2,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[37,x]*F[4,x]
F[40,x] = F[34,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[38,x]
F[44,x] = 2*F[19,x]+F[45,x]+F[64,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[38,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[48,x]+F[51,x]
F[51,x] = F[19,x]+F[52,x]+F[62,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[58,x]
F[54,x] = F[11,x]+F[55,x]
F[55,x] = F[19,x]+F[24,x]+F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[55,x]+F[7,x]
F[58,x] = F[38,x]+F[59,x]
F[59,x] = 2*F[19,x]+F[45,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[18,x]+F[59,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[2,x]+F[51,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[18,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[38,x]
F[70,x] = F[44,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[63,x]+F[73,x]
F[73,x] = F[18,x]+F[74,x]
F[74,x] = 2*F[19,x]+F[68,x]+F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[14,x]
F[78,x] = F[41,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_{17}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{71}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{33}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \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_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{23}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{44}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{45}\! \left(x \right)+F_{64}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{19}\! \left(x \right)+F_{52}\! \left(x \right)+F_{62}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55}\! \left(x \right)+F_{7}\! \left(x \right)
F_{58}\! \left(x \right) = F_{38}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{45}\! \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_{18}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right)
F_{70}\! \left(x \right) = F_{44}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{63}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{68}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right)
F_{78}\! \left(x \right) = F_{41}\! \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_17(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_11(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_71(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_33(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_30(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x) + F_27(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_13(x) + F_32(x))
Eq(F_32(x), F_23(x))
Eq(F_33(x), F_34(x) + F_44(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_2(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_37(x)*F_4(x))
Eq(F_40(x), F_34(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_38(x))
Eq(F_44(x), 2*F_19(x) + F_45(x) + F_64(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_38(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_48(x) + F_51(x))
Eq(F_51(x), F_19(x) + F_52(x) + F_62(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_58(x))
Eq(F_54(x), F_11(x) + F_55(x))
Eq(F_55(x), F_19(x) + F_24(x) + F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_55(x) + F_7(x))
Eq(F_58(x), F_38(x) + F_59(x))
Eq(F_59(x), 2*F_19(x) + F_45(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_18(x) + F_59(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_2(x) + F_51(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_18(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_38(x))
Eq(F_70(x), F_44(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_63(x) + F_73(x))
Eq(F_73(x), F_18(x) + F_74(x))
Eq(F_74(x), 2*F_19(x) + F_68(x) + F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_14(x))
Eq(F_78(x), F_41(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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": [1, 2, 0], "pos": [[0, 0], [0, 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