0123_0132_0321_1203_2103
Counting sequence:
1, 1, 2, 6, 19, 52, 134, 354, 959, 2597, 6983, 18739, 50358, 135465, 364366, 979733, 2634211, 7083138, 19046628, 51216085, 137717288, 370313804, 995756002, 2677544005, 7199793455, 19359903719, 52057864155, 139981155396, 376402782249, 1012129448698, 2721568604941, 7318170317293, 19678216864368, 52913802606742, 142282734283843, 382591601009616, 1028770876040678, 2766316649323018, 7438495765062179, 20001766339895597, 53783811853393243, 144622148282597263, 388882175759600206, 1045685936901432201, 2811800454708247626, 7560799584351545981, 20330635575172257019, 54668125808571146034, 147000027046439447224, 395276180261180995433, 1062879115202496773492, 2858032105013834727696, 7685114324345162601930, 20664912082213655491849, 55566979662596432409479, 149417002914857987551971, 401775315045358831696687, 1080354983908900242237460, 2905023896565251217486545, 7811473048498266101581230, 21004684766814004220357445, 56480612480388340468728781, 151873718723923906158016416, 408381308666625908450446066, 1098118191017829512785729743, 2952788327608434775139299756, 7939909364017677455536705594, 21350043997185406829763425258, 57409267257819263654882555927, 154370827878116318260606608757, 415095918098994197702736159335, 1116173460950084621375446606843, 3001338101889440940684165473686, 8070457430680796403000794105145, 21701081627367463063485178601446, 58353190986094950069884922710517, 156908994525207067068735596745475, 421920929204682104426826858515234, 1134525595805435523045564958760892, 3050686132029391697307429958852445, 8203151969920379904019245239044176, 22057891021664856917339527871995876, 59312634717453074682581714696792114, 159488893732892039123590399862865645, 428858157209071612996377226001576911, 1153179476639822963690443615062292959, 3100845542958851117510600556762435875, 8338028274059319305492870942190064900, 22420567079479073701443480879066683881, 60287853631934633896891915696295896178, 162111211668336714557335768922144370605, 435909447183498022957886321560748855709, 1172140064763556744850325412456634416624, 3151829675408618721673459549156373967966, 8475122215697220737096546044686466564475, 22789206260548477071750149424717759339096, 61279107105253329684254927265199845742078, 164776645780673754038993704750081292900266, 443076674535977398778251198496455997003723, 1191412403060858833245517542045862101547277, 3203652089457919044113741206048153172375091
Generating function in Maple syntax:
-(2*x^3+x^2-1)/(4*x^9+10*x^8+8*x^7-2*x^6-8*x^5-5*x^4-4*x^3-2*x^2-x+1)
Generating function in latex syntax:
-\frac{2 x^{3}+x^{2}-1}{4 x^{9}+10 x^{8}+8 x^{7}-2 x^{6}-8 x^{5}-5 x^{4}-4 x^{3}-2 x^{2}-x +1}
Generating function in sympy syntax:
(-2*x**3 - x**2 + 1)/(4*x**9 + 10*x**8 + 8*x**7 - 2*x**6 - 8*x**5 - 5*x**4 - 4*x**3 - 2*x**2 - x + 1)
Implicit equation for the generating function in Maple syntax:
(4*x^9+10*x^8+8*x^7-2*x^6-8*x^5-5*x^4-4*x^3-2*x^2-x+1)*F(x)+2*x^3+x^2-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{9}+10 x^{8}+8 x^{7}-2 x^{6}-8 x^{5}-5 x^{4}-4 x^{3}-2 x^{2}-x +1\right) F \! \left(x \right)+2 x^{3}+x^{2}-1 = 0
Explicit closed form in Maple syntax:
-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+7)-531374572/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+7)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+6)-6880792614/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+6)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+5)-475066916/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+5)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+4)-58665571/5725542899*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+4)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+3)-805421045/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+3)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+2)+785664660/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+2)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+1)+6128277060/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n-1)+2115360020/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n-1)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n)+6152067710/40078800293*RootOf(4*_Z^9+10*_Z^8+8*_Z^7-2*_Z^6-8*_Z^5-5*_Z^4-4*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n)
Explicit closed form in latex syntax:
-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +7}}{5725542899}-\frac{531374572 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +7}}{5725542899}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{40078800293}-\frac{6880792614 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +6}}{40078800293}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{5725542899}-\frac{475066916 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{5725542899}-\frac{58665571 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +4}}{5725542899}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{40078800293}-\frac{805421045 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +3}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{40078800293}+\frac{785664660 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{40078800293}+\frac{6128277060 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{40078800293}+\frac{2115360020 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{40078800293}+\frac{6152067710 \mathit{RootOf}\! \left(4 \textit{\_Z}^{9}+10 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-2 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{40078800293}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(6) = 134
a(7) = 354
a(8) = 959
a(n+9) = -4*a(n)-10*a(n+1)-8*a(n+2)+2*a(n+3)+8*a(n+4)+5*a(n+5)+4*a(n+6)+2*a(n+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) = 19
a \! \left(5\right) = 52
a \! \left(6\right) = 134
a \! \left(7\right) = 354
a \! \left(8\right) = 959
a \! \left(n +9\right) = -4 a \! \left(n \right)-10 a \! \left(n +1\right)-8 a \! \left(n +2\right)+2 a \! \left(n +3\right)+8 a \! \left(n +4\right)+5 a \! \left(n +5\right)+4 a \! \left(n +6\right)+2 a \! \left(n +7\right)+a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16236/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[15,x]+F[21,x]+F[72,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[36,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[15,x]+F[25,x]+F[29,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[18,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[12,x]+F[28,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[16,x]
F[34,x] = F[35,x]
F[35,x] = F[33,x]*F[4,x]
F[36,x] = F[37,x]+F[50,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[2,x]*F[4,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[40,x]
F[46,x] = 2*F[15,x]+F[47,x]+F[49,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[41,x]
F[49,x] = F[4,x]*F[44,x]
F[50,x] = 2*F[15,x]+F[51,x]+F[66,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[48,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[15,x]+F[45,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[12,x]+F[60,x]
F[60,x] = F[15,x]+F[25,x]+F[61,x]
F[61,x] = F[31,x]*F[4,x]
F[62,x] = F[44,x]+F[63,x]
F[63,x] = 2*F[15,x]+F[51,x]+F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[54,x]+F[56,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[65,x]+F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[47,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[69,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[40,x]+F[74,x]
F[74,x] = F[56,x]+F[75,x]
F[75,x] = 2*F[15,x]+F[47,x]+F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)+F_{72}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{50}\! \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_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{41}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{66}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)+F_{57}\! \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_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{44}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{47}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{40}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{56}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_15(x) + F_21(x) + F_72(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_36(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_29(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_18(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_12(x) + F_28(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_16(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_33(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_50(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_2(x)*F_4(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_40(x))
Eq(F_46(x), 2*F_15(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_41(x))
Eq(F_49(x), F_4(x)*F_44(x))
Eq(F_50(x), 2*F_15(x) + F_51(x) + F_66(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_48(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_15(x) + F_45(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_12(x) + F_60(x))
Eq(F_60(x), F_15(x) + F_25(x) + F_61(x))
Eq(F_61(x), F_31(x)*F_4(x))
Eq(F_62(x), F_44(x) + F_63(x))
Eq(F_63(x), 2*F_15(x) + F_51(x) + F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_54(x) + F_56(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_65(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_47(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_69(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_40(x) + F_74(x))
Eq(F_74(x), F_56(x) + F_75(x))
Eq(F_75(x), 2*F_15(x) + F_47(x) + F_55(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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, 1, 3, 2], "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, 2, 0, 3], "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, 1, 3, 2], "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, 2, 0, 3], "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": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "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, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "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, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[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": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "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, 2, 0, 3], "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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 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