0123_0213_0231_0321_2031
Counting sequence:
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
Generating function in Maple syntax:
-(x-1)*(2*x-1)^2/(x^5+3*x^4-10*x^3+12*x^2-6*x+1)
Generating function in latex syntax:
-\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}
Generating function in sympy syntax:
(1 - x)*(2*x - 1)**2/(x**5 + 3*x**4 - 10*x**3 + 12*x**2 - 6*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^5+3*x^4-10*x^3+12*x^2-6*x+1)*F(x)+(x-1)*(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\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
Explicit closed form in Maple syntax:
-109470400/174741961*((((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)*((((-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)+16971/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+43637/20800)*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+(16971/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 4)+43637/20800)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-4031/2600-47569/20800*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 = 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)-791/5200-14537/10400*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))*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)+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)^2-19387/10400)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 1)+(-791/5200-14537/10400*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))*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)^2+(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)^2-19387/10400)*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 2)-791/5200*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)^2+22613/20800-19387/10400*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)^(-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)-187709/20800*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+67943/5200)*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 = 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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)+10347/2600*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)-44237/5200)*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)+27011/10400*RootOf(_Z^5+3*_Z^4-10*_Z^3+12*_Z^2-6*_Z+1,index = 3)+53497/20800)*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))
Explicit closed form in latex syntax:
-\frac{109470400 \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) \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{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}+\frac{43637}{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)^{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{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}+\frac{43637}{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{4031}{2600}-\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}\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{791}{5200}-\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}\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{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}-\frac{19387}{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{791}{5200}-\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}\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 \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}-\frac{19387}{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{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}+\frac{22613}{20800}-\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}\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{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}+\frac{67943}{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)^{-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{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}-\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} =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{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}-\frac{109493}{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 +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{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}-\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)^{-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{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}-\frac{51409}{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)^{-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{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}+\frac{288347}{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 +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{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}-\frac{74877}{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 +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{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}-\frac{4973}{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 +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(\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) \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) \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{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}-\frac{55311}{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)+\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{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}-\frac{55311}{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{66433}{10400}+\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}\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{18287}{20800}+\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}\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{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}+\frac{18747}{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} =1\right)+\left(\frac{18287}{20800}+\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}\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 \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}+\frac{18747}{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{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}-\frac{3067}{1300}+\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}\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{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}+\frac{4973}{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)^{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{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}-\frac{44237}{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)^{-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{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}+\frac{53497}{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}+\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)}{174741961}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = -a(n)-3*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4), n >= 5
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(n +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
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16692/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[17,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[63,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[26,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[11,x]
F[26,x] = F[18,x]+F[27,x]
F[27,x] = 2*F[19,x]+F[28,x]+F[32,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[23,x]
F[31,x] = F[27,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[19,x]+F[35,x]+F[45,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[11,x]+F[38,x]
F[38,x] = F[24,x]
F[39,x] = F[34,x]+F[40,x]
F[40,x] = 2*F[19,x]+F[32,x]+F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[38,x]
F[44,x] = F[40,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[19,x]+F[48,x]+F[62,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[54,x]
F[50,x] = F[4,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[4,x]
F[54,x] = F[47,x]+F[55,x]
F[55,x] = 2*F[19,x]+F[56,x]+F[60,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[51,x]
F[59,x] = F[55,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[47,x]
F[62,x] = F[2,x]*F[4,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[2,x]+F[34,x]
F[66,x] = F[67,x]
F[67,x] = F[19,x]+F[68,x]+F[78,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[72,x]
F[70,x] = F[15,x]+F[71,x]
F[71,x] = F[52,x]
F[72,x] = F[67,x]+F[73,x]
F[73,x] = 2*F[19,x]+F[60,x]+F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[71,x]
F[77,x] = F[73,x]
F[78,x] = F[4,x]*F[46,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{45}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right)
F_{39}\! \left(x \right) = F_{34}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)+F_{62}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{19}\! \left(x \right)+F_{68}\! \left(x \right)+F_{78}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{71}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_63(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_26(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_11(x))
Eq(F_26(x), F_18(x) + F_27(x))
Eq(F_27(x), 2*F_19(x) + F_28(x) + F_32(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_23(x))
Eq(F_31(x), F_27(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_19(x) + F_35(x) + F_45(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_11(x) + F_38(x))
Eq(F_38(x), F_24(x))
Eq(F_39(x), F_34(x) + F_40(x))
Eq(F_40(x), 2*F_19(x) + F_32(x) + F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_38(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_19(x) + F_48(x) + F_62(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_54(x))
Eq(F_50(x), F_4(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_4(x))
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), 2*F_19(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_51(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_2(x)*F_4(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_2(x) + F_34(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_19(x) + F_68(x) + F_78(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_72(x))
Eq(F_70(x), F_15(x) + F_71(x))
Eq(F_71(x), F_52(x))
Eq(F_72(x), F_67(x) + F_73(x))
Eq(F_73(x), 2*F_19(x) + F_60(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_71(x))
Eq(F_77(x), F_73(x))
Eq(F_78(x), F_4(x)*F_46(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, 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