0132_0231_1032_1203_1302<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 58, 173, 512, 1513, 4471, 13213, 39047, 115385, 340950, 1007440, 2976736, 8795434, 25987937, 76786504, 226880472, 670361116, 1980706827, 5852364841, 17291890362, 51092068530, 150960893649, 446041641804, 1317911776409, 3894011797344, 11505571135719, 33995317191215, 100445390521071, 296784301020595, 876903566578367, 2590972169724408, 7655501740857566, 22619581780653314, 66833696490117476, 197472394905689157, 583468351966961264, 1723964090751854952, 5093767598713480372, 15050469141721050501, 44469367122476515113, 131392888397118762266, 388224349443312601182, 1147079932095338979155, 3389257712714319687566, 10014182553261143585445, 29588736151221358487616, 87425339249608295237369, 258314174145366607385419, 763236530016615935896345, 2255122091844454060078439, 6663171178420952959368961, 19687559406872720276842322, 58170499454434212334336336, 171875392822792182161468100, 507837321925162434787010466, 1500498362822771432337913029, 4433497184292425840918182252, 13099579293210111446505501188, 38705105817380993424871450896, 114361322818295404868543764087, 337901470117601573622767725865, 998391769995951757382361009290, 2949931310002092617785271132354, 8716112246964883146320469198137, 25753349728552604912586324751792, 76092987727652501051755178702913, 224830666392930349211961692770992, 664303374860381389719824580982151, 1962805968291026460408879516216619, 5799469662439375469867147192363291, 17135595116841305642806934512385939, 50630253643711518304153200492404887, 149596355804833736038960997599798956, 442009827317268100141986603720487990, 1305998975669755659027631705319868230, 3858813128211678252296294427281742460, 11401570013347469880445015943765114145, 33688026460485598808925958779647194724, 99537443130534201733953623905839130524, 294101603030547933085143882529754492296, 868977042053479077899048053846352249833, 2567551797864837021404875079496744198369, 7586301957000664320481325825624618528882, 22415118335938554444030549266755200683782, 66229571781080739865673848443934412498003, 195687397789580438928376084426453667226514, 578194251055032469639626965342690460435853, 1708380793701220621701414289752152660296752, 5047723893763557709775670904066608670637625, 14914424583567201437982521499077429290445711, 44067398562298044479753964062732273249456213, 130205198676458732385746365593531426276438887, 384715102671855981186227412797223592897406249, 1136711219892146381262224494886988278019758222, 3358621453784732502318837258003286567075248864, 9923662116129524008991610676504769443109684136, 29321276943589791162801433307873858428984043034<br /><br />


Generating function in Maple syntax:<br />
-(x-1)*(2*x-1)^2/(x^5+3*x^4-10*x^3+12*x^2-6*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(x -1\right) \left(2 x -1\right)^{2}}{x^{5}+3 x^{4}-10 x^{3}+12 x^{2}-6 x +1}<br /><br />



Generating function in sympy syntax:<br />
(1 - x)*(2*x - 1)**2/(x**5 + 3*x**4 - 10*x**3 + 12*x**2 - 6*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5+3*x^4-10*x^3+12*x^2-6*x+1)*F(x)+(x-1)*(2*x-1)^2 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}+3 x^{4}-10 x^{3}+12 x^{2}-6 x +1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x -1\right)^{2} = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-109470400/174741961*((((-1+1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(37333/20800-35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-539/800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^3+((-1+1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^3+(-2101/2600+11347/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(3399/1600-146527/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+9151/2600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-291/520)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((37333/20800-35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^3+(3399/1600-146527/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(-1941/416+22317/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+43637/20800+16971/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-539/800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^3+(9151/2600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-291/520)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(43637/20800+16971/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-47569/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-4031/2600)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+1)+(((-14537/10400-1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2+35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(22493/20800+35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2-16049/4160*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2+22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-791/5200)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((22493/20800+35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2-16049/4160*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(64691/20800-16049/4160*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2-9353/2600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-19387/10400+64691/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(-14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2+22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-791/5200)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(-19387/10400+64691/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-19387/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+22613/20800-791/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)^(-n+1)+(((-1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+1)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-8259/20800+RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^4+((-3293/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+54141/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+15007/20800+54141/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^3+((8123/416*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-232777/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+7767/800-232777/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((-850353/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+224657/10400)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-585549/20800+224657/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(-187709/20800+91681/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+67943/5200-187709/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+1)+(((-1+1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(37333/20800-35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-539/800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((37333/20800-35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(16049/4160*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-76291/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+1291/800-22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-539/800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(1291/800-22493/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-18287/20800+791/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^(-n+2)+(((-1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+1)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-8259/20800+RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^3+((-3293/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+54141/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+15007/20800+54141/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((4361/400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-60239/10400)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+82279/10400-60239/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(22603/10400-95701/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-109493/20800+22603/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+2)+(((-1375/832*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+1)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-8259/20800+RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^2+((35489/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-37333/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+26899/10400-37333/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(539/800-14537/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-15201/10400+539/800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n+3)+(((-17681/1600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+29281/5200)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-88601/20800+29281/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+(-88601/20800+29281/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-51409/5200-88601/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n+1)+(((-89689/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+112299/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-4673/2600+112299/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 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4)+53143/2080-182571/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(10347/2600-209/25*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-44237/5200+10347/2600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^(-n)+(((4873/650*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-83463/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+27011/10400-83463/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+(27011/10400-83463/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+53497/20800+27011/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)^(-n)+13219/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 5)^(-n))*((((RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-3354/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-3354/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+2474/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+(-3354/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+2474/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+2474/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-1549/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+((-3354/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+2474/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+2474/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-1549/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)+(2474/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-1549/5263)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)-1549/5263*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-1301/5263)<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{109470400 \left(\left(\left(\left(-1+\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{832}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{37333}{20800}-\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}-\frac{539}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{832}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{2101}{2600}+\frac{11347 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{3399}{1600}-\frac{146527 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{9151 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{2600}-\frac{291}{520}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{37333}{20800}-\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{3399}{1600}-\frac{146527 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1941}{416}+\frac{22317 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{43637}{20800}+\frac{16971 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}-\frac{539}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{9151 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{2600}-\frac{291}{520}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{43637}{20800}+\frac{16971 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{47569 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}-\frac{4031}{2600}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{14537}{10400}-\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{832}+\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{22493}{20800}+\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{10400}-\frac{16049 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{4160}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{10400}+\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}-\frac{791}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{22493}{20800}+\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{10400}-\frac{16049 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{4160}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{64691}{20800}-\frac{16049 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{4160}-\frac{9353 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{2600}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{19387}{10400}+\frac{64691 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}+\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{10400}+\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}-\frac{791}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{19387}{10400}+\frac{64691 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}+\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{19387 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}+\frac{22613}{20800}-\frac{791 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{8259}{20800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{3293 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}+\frac{54141}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{15007}{20800}+\frac{54141 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{8123 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{416}-\frac{232777}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{7767}{800}-\frac{232777 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{850353 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}+\frac{224657}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{585549}{20800}+\frac{224657 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{187709}{20800}+\frac{91681 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{67943}{5200}-\frac{187709 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{832}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{37333}{20800}-\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}-\frac{539}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{37333}{20800}-\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{16049 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{4160}-\frac{76291}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1291}{800}-\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}-\frac{539}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1291}{800}-\frac{22493 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{18287}{20800}+\frac{791 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{8259}{20800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{3293 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}+\frac{54141}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{15007}{20800}+\frac{54141 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4361 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{400}-\frac{60239}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{82279}{10400}-\frac{60239 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{22603}{10400}-\frac{95701 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{109493}{20800}+\frac{22603 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{8259}{20800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{35489 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}-\frac{37333}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{26899}{10400}-\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{539}{800}-\frac{14537 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{15201}{10400}+\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{17681 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{1600}+\frac{29281}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{88601}{20800}+\frac{29281 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{88601}{20800}+\frac{29281 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{51409}{5200}-\frac{88601 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{89689 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}+\frac{112299}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4673}{2600}+\frac{112299 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{4673}{2600}+\frac{112299 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{288347}{20800}-\frac{4673 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{2600}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{153303 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}-\frac{45737}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{38791}{20800}-\frac{45737 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{38791}{20800}-\frac{45737 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{74877}{10400}+\frac{38791 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{1375 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{832}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{8259}{20800}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{8259}{20800}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4973}{2600}+\frac{8259 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{8259}{20800}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{26899}{10400}+\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{800}+\frac{15201}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+3\right) \left(\left(-\frac{8259}{20800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{26899}{10400}-\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{800}-\frac{15201}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{26899}{10400}+\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{8187}{1300}+\frac{19597 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{4160}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{6871}{320}-\frac{2459 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{5200}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{55311}{5200}-\frac{649 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{800}+\frac{15201}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{1617 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{800}+\frac{45603}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{55311}{5200}-\frac{649 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{19437 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)}{10400}+\frac{66433}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{539}{800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1291}{800}-\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}+\frac{76291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{800}-\frac{1291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{800}+\frac{18287}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1291}{800}-\frac{37333 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}+\frac{76291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{116159}{20800}+\frac{76291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}+\frac{2337 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{320}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{18747}{4160}-\frac{116159 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}-\frac{1291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{539 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{800}-\frac{1291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{800}+\frac{18287}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{18747}{4160}-\frac{116159 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}-\frac{1291 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{18747 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{4160}-\frac{3067}{1300}+\frac{18287 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\frac{8259}{20800}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{4973}{2600}-\frac{8259 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{24777}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{14919}{2600}-\frac{24777 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-10 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{8259}{2080}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4973}{260}+\frac{8259 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{2080}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{12673 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{650}-\frac{182571}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{53143}{2080}-\frac{182571 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{10347}{2600}-\frac{209 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{25}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{44237}{5200}+\frac{10347 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{2600}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{4873 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{650}-\frac{83463}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{27011}{10400}-\frac{83463 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{27011}{10400}-\frac{83463 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{20800}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{53497}{20800}+\frac{27011 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{10400}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}+\frac{13219 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{20800}\right) \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{3354}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3354 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}+\frac{2474}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{3354 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}+\frac{2474}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2474 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}-\frac{1549}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{3354 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}+\frac{2474}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2474 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}-\frac{1549}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{2474 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}-\frac{1549}{5263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1549 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}-10 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-6 \textit{\_Z} +1, \mathit{index} =3\right)}{5263}-\frac{1301}{5263}\right)}{174741961}<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)+10*a(n+2)-12*a(n+3)+6*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)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 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/18848/<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[12,x]*F[4,x]<br />
  
    F[4,x] = F[22,x]+F[5,x]<br />
  
    F[5,x] = F[1,x]+F[6,x]<br />
  
    F[6,x] = F[7,x]<br />
  
    F[7,x] = F[12,x]*F[8,x]<br />
  
    F[8,x] = F[13,x]+F[9,x]<br />
  
    F[9,x] = F[1,x]+F[10,x]<br />
  
    F[10,x] = F[11,x]<br />
  
    F[11,x] = F[12,x]*F[9,x]<br />
  
    F[12,x] = x<br />
  
    F[13,x] = F[14,x]+F[17,x]<br />
  
    F[14,x] = F[15,x]<br />
  
    F[15,x] = F[12,x]*F[16,x]<br />
  
    F[16,x] = F[1,x]+F[14,x]<br />
  
    F[17,x] = F[18,x]+F[19,x]+F[21,x]<br />
  
    F[18,x] = 0<br />
  
    F[19,x] = F[12,x]*F[20,x]<br />
  
    F[20,x] = F[10,x]+F[17,x]<br />
  
    F[21,x] = F[12,x]*F[13,x]<br />
  
    F[22,x] = F[2,x]+F[23,x]<br />
  
    F[23,x] = F[18,x]+F[24,x]+F[31,x]<br />
  
    F[24,x] = F[12,x]*F[25,x]<br />
  
    F[25,x] = F[26,x]+F[27,x]<br />
  
    F[26,x] = F[10,x]<br />
  
    F[27,x] = F[28,x]<br />
  
    F[28,x] = F[18,x]+F[24,x]+F[29,x]<br />
  
    F[29,x] = F[12,x]*F[30,x]<br />
  
    F[30,x] = F[2,x]+F[28,x]<br />
  
    F[31,x] = F[12,x]*F[32,x]<br />
  
    F[32,x] = F[30,x]+F[33,x]<br />
  
    F[33,x] = F[34,x]+F[43,x]<br />
  
    F[34,x] = F[18,x]+F[35,x]+F[41,x]<br />
  
    F[35,x] = F[12,x]*F[36,x]<br />
  
    F[36,x] = F[37,x]+F[38,x]<br />
  
    F[37,x] = F[12,x]<br />
  
    F[38,x] = F[39,x]<br />
  
    F[39,x] = F[18,x]+F[35,x]+F[40,x]<br />
  
    F[40,x] = F[12,x]*F[2,x]<br />
  
    F[41,x] = F[12,x]*F[42,x]<br />
  
    F[42,x] = F[2,x]+F[34,x]<br />
  
    F[43,x] = F[18,x]+F[44,x]+F[45,x]+F[47,x]<br />
  
    F[44,x] = 0<br />
  
    F[45,x] = F[12,x]*F[46,x]<br />
  
    F[46,x] = F[28,x]+F[43,x]<br />
  
    F[47,x] = F[12,x]*F[33,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_{12}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)<br />
  
    F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = x<br />
  
    F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = 0<br />
  
    F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)+F_{31}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \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_{10}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)+F_{29}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{43}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{41}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{18}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = 0<br />
  
    F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{43}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \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_12(x)*F_4(x))<br />
  
    Eq(F_4(x), F_22(x) + F_5(x))<br />
  
    Eq(F_5(x), F_1(x) + F_6(x))<br />
  
    Eq(F_6(x), F_7(x))<br />
  
    Eq(F_7(x), F_12(x)*F_8(x))<br />
  
    Eq(F_8(x), F_13(x) + F_9(x))<br />
  
    Eq(F_9(x), F_1(x) + F_10(x))<br />
  
    Eq(F_10(x), F_11(x))<br />
  
    Eq(F_11(x), F_12(x)*F_9(x))<br />
  
    Eq(F_12(x), x)<br />
  
    Eq(F_13(x), F_14(x) + F_17(x))<br />
  
    Eq(F_14(x), F_15(x))<br />
  
    Eq(F_15(x), F_12(x)*F_16(x))<br />
  
    Eq(F_16(x), F_1(x) + F_14(x))<br />
  
    Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))<br />
  
    Eq(F_18(x), 0)<br />
  
    Eq(F_19(x), F_12(x)*F_20(x))<br />
  
    Eq(F_20(x), F_10(x) + F_17(x))<br />
  
    Eq(F_21(x), F_12(x)*F_13(x))<br />
  
    Eq(F_22(x), F_2(x) + F_23(x))<br />
  
    Eq(F_23(x), F_18(x) + F_24(x) + F_31(x))<br />
  
    Eq(F_24(x), F_12(x)*F_25(x))<br />
  
    Eq(F_25(x), F_26(x) + F_27(x))<br />
  
    Eq(F_26(x), F_10(x))<br />
  
    Eq(F_27(x), F_28(x))<br />
  
    Eq(F_28(x), F_18(x) + F_24(x) + F_29(x))<br />
  
    Eq(F_29(x), F_12(x)*F_30(x))<br />
  
    Eq(F_30(x), F_2(x) + F_28(x))<br />
  
    Eq(F_31(x), F_12(x)*F_32(x))<br />
  
    Eq(F_32(x), F_30(x) + F_33(x))<br />
  
    Eq(F_33(x), F_34(x) + F_43(x))<br />
  
    Eq(F_34(x), F_18(x) + F_35(x) + F_41(x))<br />
  
    Eq(F_35(x), F_12(x)*F_36(x))<br />
  
    Eq(F_36(x), F_37(x) + F_38(x))<br />
  
    Eq(F_37(x), F_12(x))<br />
  
    Eq(F_38(x), F_39(x))<br />
  
    Eq(F_39(x), F_18(x) + F_35(x) + F_40(x))<br />
  
    Eq(F_40(x), F_12(x)*F_2(x))<br />
  
    Eq(F_41(x), F_12(x)*F_42(x))<br />
  
    Eq(F_42(x), F_2(x) + F_34(x))<br />
  
    Eq(F_43(x), F_18(x) + F_44(x) + F_45(x) + F_47(x))<br />
  
    Eq(F_44(x), 0)<br />
  
    Eq(F_45(x), F_12(x)*F_46(x))<br />
  
    Eq(F_46(x), F_28(x) + F_43(x))<br />
  
    Eq(F_47(x), F_12(x)*F_33(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, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#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;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, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#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;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, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#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;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, 2], &#34;pos&#34;: [[0, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [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], &#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;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;: [[1, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[2, 0]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [2, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [0, 1], [2, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 1], [2, 1], [2, 1]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[2, 1], [2, 1], [2, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[2, 1], [2, 1], [2, 1]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 1], [2, 1], [2, 1], [2, 1]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}, &#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], [2, 1]], [[1, 0]]], &#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, 2, 1], &#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;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, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 3, 2], &#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;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#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], &#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, 2, 1], &#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;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, 2, 1], &#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;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, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], 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