0123_0132_0231_1023_1302
Counting sequence:
1, 1, 2, 6, 19, 58, 174, 519, 1545, 4595, 13659, 40591, 120608, 358335, 1064597, 3162805, 9396260, 27914848, 82930500, 246372747, 731931974, 2174445881, 6459908980, 19191289155, 57014047811, 169379009936, 503196136587, 1494909847836, 4441122023724, 13193815545718, 39196574096094, 116446331595029, 345942176091805, 1027735159558380, 3053225744388634, 9070612559213831, 26947241732428828, 80055655804721420, 237831689414688417, 706557355893289995, 2099061308418581485, 6235952877351513883, 18525951639702647585, 55037440292893696782, 163506841262711202469, 485750917873989496141, 1443083068532298639885, 4287153489691997686260, 12736401282062972743746, 37837674346805064632096, 112409272310786517516897, 333948761903953754751166, 992104772894986347347579, 2947373946797552033286678, 8756144935087911934621739, 26013012094230867964627789, 77280219004027658625895640, 229586340392890966833601315, 682061831272156275647333784, 2026289285687539674344524896, 6019759618617046474727464148, 17883678368084895821541752180, 53129356026774881840816485237, 157838248581859121601825219585, 468910496540438582913691432910, 1393053051090886662403402619018, 4138522847048855700605106971295, 12294845011202612733101974336842, 36525886031361874626882505522614, 108512173122997212521600336736151, 322371145377969891756726665413965, 957709650275905739312473379513315, 2845191908091528479096979275540431, 8452579538628850020940880211828231, 25111171114208270756441365932161932, 74601003379536019181154879339219371, 221626848063832844934195002426934709, 658415538096945374193117975281083313, 1956040184637876163948748617222703484, 5811061529588053464438060900494576424, 17263671966386434277947263228417988300, 51287422830665592785581940687869082275, 152366179439290139001399925566622139234, 452653913096312972177819084086058381661, 1344757516368942612771603702627049604068, 3995045056522006241339537438004287778115, 11868596984485706241044336583202397724807, 35259575896442025215158332032296500850200, 104750181847279888140322097308992525130035, 311194911398393440305863568365867263269128, 924506966693812053951198619325273855207880, 2746552402237660145794870073409073610820802, 8159538402630354647018392404833756356606034, 24240595915722308488241145270972095547778161, 72014673055513646909155726172885536811841845, 213943302108709327015194592562799010439372320, 635589034499880372030811445343303507546482366, 1888226538502347157128143864890747318735725091, 5609598761422978853982381839468036976623587692, 16665160468042591639198180752961978637795468076, 49509347323650438362483467890643077298380029489
Generating function in Maple syntax:
(2*x-1)^2/(x^5-3*x^3+7*x^2-5*x+1)
Generating function in latex syntax:
\frac{\left(2 x -1\right)^{2}}{x^{5}-3 x^{3}+7 x^{2}-5 x +1}
Generating function in sympy syntax:
(2*x - 1)**2/(x**5 - 3*x**3 + 7*x**2 - 5*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^5-3*x^3+7*x^2-5*x+1)*F(x)-(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-3 x^{3}+7 x^{2}-5 x +1\right) F \! \left(x \right)-\left(2 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-177555665/2280731049*((((38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-6324/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+187/133+6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^3+((38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^3+(-65522/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-94784/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-7604/6517*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-159148/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+167354/32585+187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-6324/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^3+(-7604/6517*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-159148/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(414976/32585-49643/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+247622/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-8011/1715)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(187/133+6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^3+(167354/32585+187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(247622/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-8011/1715)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+135974/32585-8011/1715*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^(-n+1)+(((-6248/32585+32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-118372/32585+159146/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+75094/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-118372/32585+159146/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(230456/32585+159146/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-497654/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2+230456/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-91383/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+75094/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2+230456/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-91383/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+135974/32585+75094/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-91383/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)^(-n+1)+(((-38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^4+((50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+250778/32585+50516/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^3+((114474/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-3)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-151548/32585-3*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-492127/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+114818/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-767098/32585+114818/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-14764/32585+266366/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-14764/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+91148/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^(-n+1)+(((38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-6324/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+187/133+6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-6324/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-159146/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-86591/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+2636/931+118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(187/133+6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(2636/931+118372/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-75094/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-60826/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^(-n+2)+(((-38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^3+((50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+250778/32585+50516/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-121126/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+72557/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-75094/32585+72557/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-75094/32585+72557/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-75094/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-60826/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^(-n+2)+(((-38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((32937/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+6324/4655)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+204963/32585+6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-187/133-6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-167354/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^(-n+3)+(((-127266/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+38271/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-368376/32585+38271/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(-368376/32585+38271/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-368376/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-31926/931)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^(-n+1)+(((-2480/343*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+170312/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+10922/4655+170312/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(10922/4655+170312/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+10922/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+691508/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^(-n+2)+(((352/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-6248/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-187/133-6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(-187/133-6248/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-167354/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^(-n+3)+(((38158/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-1)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-50516/32585-RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(-50516/32585-RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-50516/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-250778/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^(-n+4)+(((-187/133+6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-2636/931+86591/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-2636/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+60826/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-2636/931+86591/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-295789/32585+86591/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2+355237/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-2636/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-295789/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+274431/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-2636/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+60826/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-2636/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2-295789/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+274431/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+79178/32585+60826/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^2+274431/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)^(-n)+(((-50516/32585-RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(-6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-204963/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+167354/32585+187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^3-((RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+50516/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+204963/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-167354/32585-187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((-6324/4655*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-204963/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^3+(167354/32585+187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^2+(874098/32585+539757/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)-10189/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-579224/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(167354/32585+187/133*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^3+(-10189/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-579224/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+109131/6517+274431/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)^(-n)+(((50516/32585+RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+250778/32585+50516/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^4+((-151548/32585-3*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-752334/32585-151548/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^2+((406953/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+259209/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+1963449/32585+259209/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+(-77162/32585-6262/931*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-77162/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-861146/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)^(-n)+(((178858/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-94403/32585)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+208003/32585-94403/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(208003/32585-94403/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+208003/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+88652/6517)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)^(-n)+143271/32585*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 5)^(-n))*((((RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-3850/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-3850/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+2431/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(-3850/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+2431/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+2431/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-216/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 1)+((-3850/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)+2431/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)+2431/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-216/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 2)+(2431/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-216/5449)*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 4)-216/5449*RootOf(_Z^5-3*_Z^3+7*_Z^2-5*_Z+1,index = 3)-4139/5449)
Explicit closed form in latex syntax:
-\frac{177555665 \left(\left(\left(\left(\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{6324}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{187}{133}+\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{65522 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{94784}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{7604 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6517}-\frac{159148}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{167354}{32585}+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{6324}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{7604 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{6517}-\frac{159148}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{414976}{32585}-\frac{49643 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{247622 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{8011}{1715}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{187}{133}+\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{167354}{32585}+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{247622 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{8011}{1715}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{135974}{32585}-\frac{8011 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{1715}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{6248}{32585}+\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{118372}{32585}+\frac{159146 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}-\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{75094}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{118372}{32585}+\frac{159146 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{230456}{32585}+\frac{159146 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}-\frac{497654 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}+\frac{230456 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{91383}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}-\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{75094}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}+\frac{230456 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{91383}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{135974}{32585}+\frac{75094 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}-\frac{91383 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{250778}{32585}+\frac{50516 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{114474 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{151548}{32585}-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{492127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{114818}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{767098}{32585}+\frac{114818 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{14764}{32585}+\frac{266366 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{14764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{91148}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{6324}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{187}{133}+\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{6324}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{159146 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{86591}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{2636}{931}+\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{187}{133}+\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{2636}{931}+\frac{118372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{75094 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}-\frac{60826}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{250778}{32585}+\frac{50516 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{121126 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{72557}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{75094}{32585}+\frac{72557 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{75094}{32585}+\frac{72557 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{75094 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{60826}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{32937 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{6324}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{204963}{32585}+\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{187}{133}-\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{133}-\frac{167354}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{127266 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{38271}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{368376}{32585}+\frac{38271 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{368376}{32585}+\frac{38271 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{368376 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{31926}{931}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{2480 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{343}+\frac{170312}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{10922}{4655}+\frac{170312 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{10922}{4655}+\frac{170312 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{10922 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4655}+\frac{691508}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{352 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{6248}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{187}{133}-\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{187}{133}-\frac{6248 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{133}-\frac{167354}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{38158 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{50516}{32585}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{50516}{32585}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{50516 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{250778}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\frac{187}{133}+\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{4655}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2636}{931}+\frac{86591 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{133}-\frac{2636 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{931}+\frac{60826}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{2636}{931}+\frac{86591 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{4655}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{295789}{32585}+\frac{86591 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}+\frac{355237 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{2636 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{931}-\frac{295789 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{274431}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{133}-\frac{2636 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{931}+\frac{60826}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2636 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{931}-\frac{295789 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{274431}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{79178}{32585}+\frac{60826 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{32585}+\frac{274431 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\frac{50516}{32585}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4655}-\frac{204963}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{167354}{32585}+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{50516}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4655}+\frac{204963}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{167354}{32585}-\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{6324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{4655}-\frac{204963}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{167354}{32585}+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{874098}{32585}+\frac{539757 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{10189 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{931}-\frac{579224}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{167354}{32585}+\frac{187 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{133}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{10189 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{931}-\frac{579224}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{109131}{6517}+\frac{274431 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{50516}{32585}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{250778}{32585}+\frac{50516 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{151548}{32585}-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{752334}{32585}-\frac{151548 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{406953 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{259209}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1963449}{32585}+\frac{259209 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{77162}{32585}-\frac{6262 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{931}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{77162 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{861146}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{178858 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}-\frac{94403}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{208003}{32585}-\frac{94403 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{208003}{32585}-\frac{94403 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{208003 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{32585}+\frac{88652}{6517}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}+\frac{143271 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{32585}\right) \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{3850}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3850 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}+\frac{2431}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{3850 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}+\frac{2431}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2431 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}-\frac{216}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{3850 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}+\frac{2431}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2431 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}-\frac{216}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{2431 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}-\frac{216}{5449}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{216 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{3}+7 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)}{5449}-\frac{4139}{5449}\right)}{2280731049}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n) = 3*a(n+2)-7*a(n+3)+5*a(n+4)-a(n+5), n >= 5
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(n \right) = 3 a \! \left(n +2\right)-7 a \! \left(n +3\right)+5 a \! \left(n +4\right)-a \! \left(n +5\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16074/
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[10,x]*F[4,x]
F[4,x] = F[20,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[10,x]*F[8,x]
F[8,x] = F[11,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = x
F[11,x] = F[12,x]+F[15,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = F[1,x]+F[12,x]
F[15,x] = F[16,x]+F[17,x]+F[19,x]
F[16,x] = 0
F[17,x] = F[10,x]*F[18,x]
F[18,x] = F[10,x]+F[15,x]
F[19,x] = F[10,x]*F[12,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[16,x]+F[22,x]+F[53,x]
F[22,x] = F[10,x]*F[23,x]
F[23,x] = F[24,x]+F[33,x]
F[24,x] = F[12,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[10,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[10,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[32,x]
F[32,x] = F[10,x]+F[30,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[16,x]+F[22,x]+F[35,x]
F[35,x] = F[10,x]*F[36,x]
F[36,x] = F[2,x]+F[34,x]
F[37,x] = F[38,x]
F[38,x] = F[10,x]*F[39,x]
F[39,x] = F[40,x]+F[49,x]
F[40,x] = F[41,x]
F[41,x] = F[16,x]+F[42,x]+F[48,x]
F[42,x] = F[10,x]*F[43,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[26,x]
F[46,x] = F[41,x]+F[47,x]
F[47,x] = F[38,x]
F[48,x] = F[10,x]*F[2,x]
F[49,x] = F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[10,x]*F[52,x]
F[52,x] = F[41,x]+F[50,x]
F[53,x] = F[10,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[2,x]+F[41,x]
F[56,x] = F[34,x]+F[57,x]
F[57,x] = F[16,x]+F[58,x]+F[59,x]+F[61,x]
F[58,x] = 0
F[59,x] = F[10,x]*F[60,x]
F[60,x] = F[41,x]+F[57,x]
F[61,x] = F[10,x]*F[34,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{11}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = x
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{10}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right)+F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{42}\! \left(x \right) = F_{10}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{26}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{10}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{56}\! \left(x \right) = F_{34}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right)+F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{10}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{41}\! \left(x \right)+F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{10}\! \left(x \right) F_{34}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_20(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_10(x)*F_8(x))
Eq(F_8(x), F_11(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), x)
Eq(F_11(x), F_12(x) + F_15(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), F_1(x) + F_12(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_19(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_10(x)*F_18(x))
Eq(F_18(x), F_10(x) + F_15(x))
Eq(F_19(x), F_10(x)*F_12(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_16(x) + F_22(x) + F_53(x))
Eq(F_22(x), F_10(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_33(x))
Eq(F_24(x), F_12(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_10(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_10(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_32(x))
Eq(F_32(x), F_10(x) + F_30(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_16(x) + F_22(x) + F_35(x))
Eq(F_35(x), F_10(x)*F_36(x))
Eq(F_36(x), F_2(x) + F_34(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_10(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_49(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_16(x) + F_42(x) + F_48(x))
Eq(F_42(x), F_10(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_26(x))
Eq(F_46(x), F_41(x) + F_47(x))
Eq(F_47(x), F_38(x))
Eq(F_48(x), F_10(x)*F_2(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_10(x)*F_52(x))
Eq(F_52(x), F_41(x) + F_50(x))
Eq(F_53(x), F_10(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_2(x) + F_41(x))
Eq(F_56(x), F_34(x) + F_57(x))
Eq(F_57(x), F_16(x) + F_58(x) + F_59(x) + F_61(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_10(x)*F_60(x))
Eq(F_60(x), F_41(x) + F_57(x))
Eq(F_61(x), F_10(x)*F_34(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 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], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], 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