0123_0231_0312_1302_2031<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 59, 180, 545, 1647, 4977, 15043, 45473, 137464, 415553, 1256212, 3797508, 11479796, 34703205, 104907130, 317132270, 958684865, 2898086256, 8760860065, 26483914652, 80060374207, 242021000371, 731624916824, 2211688316710, 6685892043586, 20211325475112, 61098455493741, 184699477939605, 558343036259833, 1687860461856762, 5102370323776270, 15424369199521011, 46627577009552335, 140954285368717024, 426102144654341469, 1288098742114050735, 3893898189087405097, 11771180742008411151, 35584057243546862741, 107569933523591049440, 325181879038491058773, 983018683671617109176, 2971646929726662244704, 8983232589202585475944, 27156142590309067059441, 82092506574034926933826, 248164098166611826900274, 750195385535062094263721, 2267826493178935728950816, 6855596691648668965204193, 20724339423631493100493488, 62649286978782089427598719, 189387612252397439997886315, 572515177815383865105434476, 1730702578329968621200996622, 5231881233380839489964408838, 15815878235193725305386052320, 47811101436037936800303550137, 144532057375131235989682638601, 436917681911896212834994928257, 1320793907138496397433444635314, 3992735055950310851319517622630, 12069962725337500795806251162771, 36487269540693934547993925133843, 110300327252918249353290900747772, 333435807755689839796621752574937, 1007970154419898554456639796963727, 3047074754927657496535085745214785, 9211249481350867112086783841279195, 27845433352258214199313137466446745, 84176219539473730752043719180187416, 254463123138395936015172365619636857, 769237219152872389614978771143189372, 2325389596858086799731968336462102876, 7029608867770063455789400052428341900, 21250374948180015531102631590768488941, 64239482442425956374491971941840498378, 194194743129658713804583681111809854406, 587047043739693923177064819338881784769, 1774632134781411616932579956672936452320, 5364679453518019842286093712201543958097, 16217324748570113553170023571602811600468, 49024666670086867290362817080207426003903, 148200642175895025994835877762945517350259, 448007744532998338613541315994356164501376, 1354318957156247235324335300427061774888822, 4094080649486824161359278690852058713473674, 12376328542057533083802355446595663393720552, 37413407623063702785562106738931156708881253, 113100025198330275019547176372568058228792477, 341899241810240259151102015305431566863424025, 1033554955849319240008019625070196533981261098, 3124417126825852476695228272745308735867537422, 9445054012034463155196619047924219357554070323, 28552220036278340140043647563606275996337400327, 86312822347159245334638926483949628237246841736, 260922033105182509449144120053201739044792147157<br /><br />


Generating function in Maple syntax:<br />
-(x-1)*(x^3-2*x^2+3*x-1)/(x^5-3*x^4+7*x^3-8*x^2+5*x-1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}{x^{5}-3 x^{4}+7 x^{3}-8 x^{2}+5 x -1}<br /><br />



Generating function in sympy syntax:<br />
(1 - x)*(x**3 - 2*x**2 + 3*x - 1)/(x**5 - 3*x**4 + 7*x**3 - 8*x**2 + 5*x - 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-3*x^4+7*x^3-8*x^2+5*x-1)*F(x)+(x-1)*(x^3-2*x^2+3*x-1) = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-3 x^{4}+7 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) = 0<br /><br />



Explicit closed form in Maple syntax:<br />
29241/6848689*((((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-22/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-22/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+31/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+31/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-250/171)*((((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+56/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(49/171-214/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(2213/171+14/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1454/171-310/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(2213/171+14/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(232/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-6491/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+196/9-91/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(56/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-1454/171-310/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(196/9-91/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1021/171-134/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+1)+(((-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-53/57-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-122/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-116/9*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+1061/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+910/171-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+1061/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-53/57-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(910/171-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+1061/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-680/171-53/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+910/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+1)+(((1-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((-220/171+179/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-220/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-2467/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((106/57-1367/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+106/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+6815/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((364/57+764/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+364/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-11642/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-959/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-526/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3341/57-526/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+1)+(((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+56/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-1-35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(1766/171-142/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1127/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(56/171+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1127/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-63/19+53/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+2)+(((1-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((-220/171+179/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-220/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-2467/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-149/57-136/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-149/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1697/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(48/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+109/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1475/57+109/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+2)+(((1-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((1+35/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-548/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1286/171-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+3)+(((409/171-1409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+202/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(409/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+202/19)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-2681/171+202/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+1)+(((-85/19+959/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-85/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1724/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-85/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1724/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+6691/171-1724/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+2)+(((391/171-48/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+391/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+823/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(391/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+823/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-3478/171+823/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+3)+(((-1+122/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1588/171-293/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+4)+(((-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(548/57-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1286/171+56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3-((293/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-548/57+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1286/171-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*(RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((548/57-RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-6218/171+569/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-854/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+13576/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-6983/171+1679/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-1286/171+56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(1286/57-56/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-6983/171+1679/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3472/171+895/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n)+(((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-56/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1127/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+63/19-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1127/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(4990/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1766/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1135/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-806/171+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1135/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(63/19-56/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-806/171+1127/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1135/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1012/171+63/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-806/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n)+(((RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+293/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1588/171+293/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((-293/57-3*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-293/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1588/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((2051/171+7*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+2051/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)-11116/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-1790/171-7*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1790/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+13087/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(143/19*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+673/57)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-13358/171+673/57*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n)+(((554/171+RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)+554/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+383/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(554/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3)+383/171)*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 4)-5711/171+383/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n)-2617/171*RootOf(_Z^5-3*_Z^4+7*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
\frac{29241 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{122}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{22}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{22 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{31}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{31 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{250}{171}\right) \left(\left(\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{56}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{49}{171}-\frac{214 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2213}{171}+\frac{14 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1454}{171}-\frac{310 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{2213}{171}+\frac{14 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{9}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{232 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{6491}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{196}{9}-\frac{91 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{56}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{1454}{171}-\frac{310 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{196}{9}-\frac{91 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1021}{171}-\frac{134 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{122}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{53}{57}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{122}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{116 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{9}+\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{1061}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{910}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{1061 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{53}{57}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{910}{171}-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{1061 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{680}{171}-\frac{53 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{57}+\frac{910 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{220}{171}+\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{220 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{2467}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{106}{57}-\frac{1367 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{106 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{6815}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{364}{57}+\frac{764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{364 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}-\frac{11642}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{959 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{526}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3341}{57}-\frac{526 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{56}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-1-\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1766}{171}-\frac{142 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1127}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{56}{171}+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}-\frac{1127}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{63}{19}+\frac{53 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{220}{171}+\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{220 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{2467}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{149}{57}-\frac{136 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{149 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{1697}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{48 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}+\frac{109}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1475}{57}+\frac{109 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(1+\frac{35 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{548}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1286}{171}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{409}{171}-\frac{1409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{202}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{409 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{202}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2681}{171}+\frac{202 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{85}{19}+\frac{959 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{85 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}-\frac{1724}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{85 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}-\frac{1724}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6691}{171}-\frac{1724 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{391}{171}-\frac{48 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{391 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{823}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{391 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{823}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3478}{171}+\frac{823 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{122 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1588}{171}-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{548}{57}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1286}{171}+\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(\frac{293}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{548}{57}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1286}{171}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{548}{57}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{6218}{171}+\frac{569 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{854 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}+\frac{13576}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{6983}{171}+\frac{1679 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1286}{171}+\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{1286}{57}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{6983}{171}+\frac{1679 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3472}{171}+\frac{895 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{56}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1127}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{63}{19}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{1127}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{4990 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{1766 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{1135}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{806}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{1135 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{63}{19}-\frac{56 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{806}{171}+\frac{1127 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{171}-\frac{1135 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1012}{171}+\frac{63 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{19}-\frac{806 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{293}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1588}{171}+\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{293}{57}-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}+\frac{1588}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{2051}{171}+7 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2051 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}-\frac{11116}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1790}{171}-7 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1790 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{13087}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{143 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{19}+\frac{673}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{13358}{171}+\frac{673 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{57}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{554}{171}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{554 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{383}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{554 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}+\frac{383}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{5711}{171}+\frac{383 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{171}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+7 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{171}\right)}{6848689}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 19<br />
    
    a(n+5) = a(n)-3*a(n+1)+7*a(n+2)-8*a(n+3)+5*a(n+4), n >= 5<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 19<br />
    
    a \! \left(n +5\right) = a \! \left(n \right)-3 a \! \left(n +1\right)+7 a \! \left(n +2\right)-8 a \! \left(n +3\right)+5 a \! \left(n +4\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/17036/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[17,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[13,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[10,x]*F[4,x]<br />
  
    F[13,x] = F[11,x]+F[14,x]<br />
  
    F[14,x] = F[15,x]<br />
  
    F[15,x] = F[16,x]*F[4,x]<br />
  
    F[16,x] = F[11,x]+F[14,x]<br />
  
    F[17,x] = F[18,x]+F[2,x]<br />
  
    F[18,x] = F[19,x]+F[20,x]+F[55,x]<br />
  
    F[19,x] = 0<br />
  
    F[20,x] = F[21,x]*F[4,x]<br />
  
    F[21,x] = F[22,x]+F[28,x]<br />
  
    F[22,x] = F[23,x]+F[7,x]<br />
  
    F[23,x] = F[24,x]<br />
  
    F[24,x] = F[25,x]*F[4,x]<br />
  
    F[25,x] = F[26,x]+F[27,x]<br />
  
    F[26,x] = F[11,x]<br />
  
    F[27,x] = F[14,x]<br />
  
    F[28,x] = F[18,x]+F[29,x]<br />
  
    F[29,x] = 2*F[19,x]+F[30,x]+F[34,x]<br />
  
    F[30,x] = F[31,x]*F[4,x]<br />
  
    F[31,x] = F[32,x]+F[33,x]<br />
  
    F[32,x] = F[23,x]<br />
  
    F[33,x] = F[29,x]<br />
  
    F[34,x] = F[35,x]*F[4,x]<br />
  
    F[35,x] = F[36,x]+F[51,x]<br />
  
    F[36,x] = F[37,x]<br />
  
    F[37,x] = F[19,x]+F[38,x]+F[48,x]<br />
  
    F[38,x] = F[39,x]*F[4,x]<br />
  
    F[39,x] = F[40,x]+F[42,x]<br />
  
    F[40,x] = F[11,x]+F[41,x]<br />
  
    F[41,x] = F[24,x]<br />
  
    F[42,x] = F[37,x]+F[43,x]<br />
  
    F[43,x] = 2*F[19,x]+F[34,x]+F[44,x]<br />
  
    F[44,x] = F[4,x]*F[45,x]<br />
  
    F[45,x] = F[46,x]+F[47,x]<br />
  
    F[46,x] = F[41,x]<br />
  
    F[47,x] = F[43,x]<br />
  
    F[48,x] = F[4,x]*F[49,x]<br />
  
    F[49,x] = F[2,x]+F[50,x]<br />
  
    F[50,x] = F[48,x]<br />
  
    F[51,x] = F[52,x]<br />
  
    F[52,x] = F[53,x]<br />
  
    F[53,x] = F[4,x]*F[54,x]<br />
  
    F[54,x] = F[37,x]+F[52,x]<br />
  
    F[55,x] = F[4,x]*F[56,x]<br />
  
    F[56,x] = F[57,x]+F[58,x]<br />
  
    F[57,x] = F[2,x]+F[37,x]<br />
  
    F[58,x] = F[50,x]+F[52,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{55}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = 0<br />
  
    F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{11}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{14}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{23}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{29}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{51}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{11}\! \left(x \right)+F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{24}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{43}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{48}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{53}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{37}\! \left(x \right)+F_{52}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_17(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_13(x))<br />
  
    Eq(F_10(x), F_1(x) + F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_10(x)*F_4(x))<br />
  
    Eq(F_13(x), F_11(x) + F_14(x))<br />
  
    Eq(F_14(x), F_15(x))<br />
  
    Eq(F_15(x), F_16(x)*F_4(x))<br />
  
    Eq(F_16(x), F_11(x) + F_14(x))<br />
  
    Eq(F_17(x), F_18(x) + F_2(x))<br />
  
    Eq(F_18(x), F_19(x) + F_20(x) + F_55(x))<br />
  
    Eq(F_19(x), 0)<br />
  
    Eq(F_20(x), F_21(x)*F_4(x))<br />
  
    Eq(F_21(x), F_22(x) + F_28(x))<br />
  
    Eq(F_22(x), F_23(x) + F_7(x))<br />
  
    Eq(F_23(x), F_24(x))<br />
  
    Eq(F_24(x), F_25(x)*F_4(x))<br />
  
    Eq(F_25(x), F_26(x) + F_27(x))<br />
  
    Eq(F_26(x), F_11(x))<br />
  
    Eq(F_27(x), F_14(x))<br />
  
    Eq(F_28(x), F_18(x) + F_29(x))<br />
  
    Eq(F_29(x), 2*F_19(x) + F_30(x) + F_34(x))<br />
  
    Eq(F_30(x), F_31(x)*F_4(x))<br />
  
    Eq(F_31(x), F_32(x) + F_33(x))<br />
  
    Eq(F_32(x), F_23(x))<br />
  
    Eq(F_33(x), F_29(x))<br />
  
    Eq(F_34(x), F_35(x)*F_4(x))<br />
  
    Eq(F_35(x), F_36(x) + F_51(x))<br />
  
    Eq(F_36(x), F_37(x))<br />
  
    Eq(F_37(x), F_19(x) + F_38(x) + F_48(x))<br />
  
    Eq(F_38(x), F_39(x)*F_4(x))<br />
  
    Eq(F_39(x), F_40(x) + F_42(x))<br />
  
    Eq(F_40(x), F_11(x) + F_41(x))<br />
  
    Eq(F_41(x), F_24(x))<br />
  
    Eq(F_42(x), F_37(x) + F_43(x))<br />
  
    Eq(F_43(x), 2*F_19(x) + F_34(x) + F_44(x))<br />
  
    Eq(F_44(x), F_4(x)*F_45(x))<br />
  
    Eq(F_45(x), F_46(x) + F_47(x))<br />
  
    Eq(F_46(x), F_41(x))<br />
  
    Eq(F_47(x), F_43(x))<br />
  
    Eq(F_48(x), F_4(x)*F_49(x))<br />
  
    Eq(F_49(x), F_2(x) + F_50(x))<br />
  
    Eq(F_50(x), F_48(x))<br />
  
    Eq(F_51(x), F_52(x))<br />
  
    Eq(F_52(x), F_53(x))<br />
  
    Eq(F_53(x), F_4(x)*F_54(x))<br />
  
    Eq(F_54(x), F_37(x) + F_52(x))<br />
  
    Eq(F_55(x), F_4(x)*F_56(x))<br />
  
    Eq(F_56(x), F_57(x) + F_58(x))<br />
  
    Eq(F_57(x), F_2(x) + F_37(x))<br />
  
    Eq(F_58(x), F_50(x) + F_52(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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&#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], 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{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2], 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0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 4], [1, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 3], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, 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{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: 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[0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: 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1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], 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[[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 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[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 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&#34;strategy_class&#34;: &#34;EmptyStrategy&#34;}}]}<br /><br />