0132_1302_2103
Counting sequence:
1, 1, 2, 6, 21, 73, 245, 804, 2617, 8511, 27709, 90283, 294231, 958826, 3124175, 10178664, 33160777, 108030912, 351937426, 1146512182, 3734982701, 12167348792, 39637060036, 129123584284, 420638265356, 1370286347625, 4463889391210, 14541700425059, 47371455692470, 154318538952999, 502712122814838, 1637647892985070, 5334843017892219, 17378917297845870, 56613989369292786, 184427118373696840, 600794277295120524, 1957162038070501734, 6375698507962810093, 20769629789262275801, 67659648164133063250, 220409704363737546537, 718011974410418142890, 2339013135984602501146, 7619625623686163832556, 24821876227109680723511, 80860342644694303535393, 263412602161426341970201, 858099244569336353913886, 2795364789684756879894282, 9106247738459114229555151, 29664732189448731403058592, 96636546799830038880648563, 314805544740082171073735897, 1025518132362450160836289416, 3340752592588372492825286605, 10882916188697851283411057731, 35452450154496950490251737737, 115490756350764438209763970918, 376225472264325526845205734204, 1225601168887914255100232572379, 3992547915826768381332090677581, 13006220347003138787203552211460, 42369376969450356488880084826419, 138023503898960003462272911027380, 449628693909084289115452677035665, 1464721273372062360917651989620595, 4771511333083974513181343663676351, 15543790354953418356434531624392521, 50635826205296899871936523164880783, 164952488224676428843715209588861690, 537353202477421899831999097007596916, 1750494747429359092914323953008083480, 5702453891872378030136380364206830071, 18576451278520797761355261016467293218, 60515095544232799313202066820812840590, 197135434202215032412153746648963746156, 642193143191665966936910437002658765817, 2092023865883721871062476061545251259431, 6815027382067214985833194811492409992820, 22200797503190125665928502030556284166651, 72321853185004350670820045560632003367608, 235597412541676224722524931858746194431743, 767487811109375333523841033417836176289610, 2500186796819173309376858631391747785525215, 8144668786274811508061199679801002552463701, 26532269397836067115025967625981676951902557, 86432160456376736164289404793259603734441338, 281563489694030259914484996616284388559267072, 917228012236171402645829694087469937980314768, 2987984086093515388984403168004121401339873736, 9733728996110587672856154612734332947210283368, 31708830248019852093157648894927950587034665425, 103295449883543830306521010470164309080638330916, 336497747888698278649595304221565709268416643421, 1096183176140122674873872492683899472652594746685, 3570952742453718754188247596438198621088748907968, 11632821745849995220147655008615925228868988569426, 37895360574762457164632073912163589111920365729004, 123448840226884250622824591216242886149963091888049, 402149918148874160544616507861139567698507846518670
Generating function in Maple syntax:
-(x-1)*(3*x^3-5*x^2+4*x-1)^2/(x^9+2*x^8-27*x^7+86*x^6-144*x^5+150*x^4-100*x^3+42*x^2-10*x+1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2}}{x^{9}+2 x^{8}-27 x^{7}+86 x^{6}-144 x^{5}+150 x^{4}-100 x^{3}+42 x^{2}-10 x +1}
Generating function in sympy syntax:
(1 - x)*(3*x**3 - 5*x**2 + 4*x - 1)**2/(x**9 + 2*x**8 - 27*x**7 + 86*x**6 - 144*x**5 + 150*x**4 - 100*x**3 + 42*x**2 - 10*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^9+2*x^8-27*x^7+86*x^6-144*x^5+150*x^4-100*x^3+42*x^2-10*x+1)*F(x)+(x-1)*(3*x^3-5*x^2+4*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{9}+2 x^{8}-27 x^{7}+86 x^{6}-144 x^{5}+150 x^{4}-100 x^{3}+42 x^{2}-10 x +1\right) F \! \left(x \right)+\left(x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+7)-7957283969/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+7)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+6)-17392853887/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+6)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+5)+213069428733/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+5)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+4)-640837687333/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+4)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+3)+988919094792/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+3)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+2)-915632090270/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+2)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n+1)+508840098203/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n+1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n-1)+21034580874/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n-1)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 1)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 2)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 3)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 4)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 5)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 6)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 7)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 8)^(-n)-158274501633/17682055219*RootOf(_Z^9+2*_Z^8-27*_Z^7+86*_Z^6-144*_Z^5+150*_Z^4-100*_Z^3+42*_Z^2-10*_Z+1,index = 9)^(-n)
Explicit closed form in latex syntax:
-\frac{7957283969 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{17682055219}-\frac{7957283969 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{17682055219}-\frac{7957283969 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{17682055219}-\frac{7957283969 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{17682055219}-\frac{7957283969 \mathit{RootOf}\! 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\left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{17682055219}+\frac{213069428733 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +5}}{17682055219}-\frac{640837687333 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{17682055219}-\frac{640837687333 \mathit{RootOf}\! 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\left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{17682055219}-\frac{640837687333 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{17682055219}-\frac{640837687333 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{17682055219}-\frac{640837687333 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +4}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{17682055219}+\frac{988919094792 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +3}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{17682055219}-\frac{915632090270 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{17682055219}+\frac{508840098203 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{17682055219}+\frac{21034580874 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{17682055219}-\frac{158274501633 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}-27 \textit{\_Z}^{7}+86 \textit{\_Z}^{6}-144 \textit{\_Z}^{5}+150 \textit{\_Z}^{4}-100 \textit{\_Z}^{3}+42 \textit{\_Z}^{2}-10 \textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{17682055219}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 245
a(7) = 804
a(8) = 2617
a(n+9) = -a(n)-2*a(n+1)+27*a(n+2)-86*a(n+3)+144*a(n+4)-150*a(n+5)+100*a(n+6)-42*a(n+7)+10*a(n+8), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 245
a \! \left(7\right) = 804
a \! \left(8\right) = 2617
a \! \left(n +9\right) = -a \! \left(n \right)-2 a \! \left(n +1\right)+27 a \! \left(n +2\right)-86 a \! \left(n +3\right)+144 a \! \left(n +4\right)-150 a \! \left(n +5\right)+100 a \! \left(n +6\right)-42 a \! \left(n +7\right)+10 a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14731/
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[28,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[27,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[22,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]*F[4,x]
F[27,x] = F[13,x]*F[4,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[108,x]+F[15,x]+F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[56,x]
F[32,x] = F[33,x]+F[7,x]
F[33,x] = F[15,x]+F[16,x]+F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[13,x]+F[36,x]
F[36,x] = F[37,x]+F[54,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[24,x]+F[40,x]
F[40,x] = F[37,x]+F[41,x]
F[41,x] = 2*F[15,x]+F[42,x]+F[53,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[22,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[44,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[37,x]+F[48,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[47,x]
F[53,x] = F[4,x]*F[40,x]
F[54,x] = 2*F[15,x]+F[42,x]+F[55,x]
F[55,x] = F[36,x]*F[4,x]
F[56,x] = F[57,x]+F[77,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[2,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[60,x]
F[63,x] = F[57,x]+F[64,x]
F[64,x] = 2*F[15,x]+F[65,x]+F[76,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[67,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[57,x]+F[71,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[70,x]
F[76,x] = F[4,x]*F[63,x]
F[77,x] = 2*F[15,x]+F[78,x]+F[86,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[61,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[80,x]
F[83,x] = F[71,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[83,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[63,x]+F[88,x]
F[88,x] = F[106,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[73,x]+F[92,x]
F[92,x] = F[89,x]+F[93,x]
F[93,x] = 3*F[15,x]+F[105,x]+F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]+F[99,x]
F[96,x] = F[71,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[96,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[100,x]+F[89,x]
F[103,x] = F[104,x]
F[104,x] = F[4,x]*F[99,x]
F[105,x] = F[4,x]*F[92,x]
F[106,x] = 3*F[15,x]+F[107,x]+F[94,x]
F[107,x] = F[4,x]*F[88,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[118,x]
F[110,x] = F[111,x]+F[2,x]
F[111,x] = F[112,x]+F[117,x]+F[15,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[11,x]+F[14,x]
F[115,x] = F[116,x]+F[61,x]
F[116,x] = 2*F[15,x]+F[76,x]+F[78,x]
F[117,x] = F[110,x]*F[4,x]
F[118,x] = F[119,x]+F[57,x]
F[119,x] = 2*F[15,x]+F[120,x]+F[65,x]
F[120,x] = F[118,x]*F[4,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_{28}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{108}\! \left(x \right)+F_{15}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{56}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{54}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{53}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{37}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{77}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{65}\! \left(x \right)+F_{76}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{57}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{61}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{71}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{63}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{106}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{105}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{71}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)+F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{105}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{106}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{107}\! \left(x \right)+F_{94}\! \left(x \right)
F_{107}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{118}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{2}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{117}\! \left(x \right)+F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{61}\! \left(x \right)
F_{116}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{57}\! \left(x \right)
F_{119}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{120}\! \left(x \right)+F_{65}\! \left(x \right)
F_{120}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \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_28(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_27(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_22(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_21(x)*F_4(x))
Eq(F_27(x), F_13(x)*F_4(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_108(x) + F_15(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_56(x))
Eq(F_32(x), F_33(x) + F_7(x))
Eq(F_33(x), F_15(x) + F_16(x) + F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_13(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_54(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_24(x) + F_40(x))
Eq(F_40(x), F_37(x) + F_41(x))
Eq(F_41(x), 2*F_15(x) + F_42(x) + F_53(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_22(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_44(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_37(x) + F_48(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_47(x))
Eq(F_53(x), F_4(x)*F_40(x))
Eq(F_54(x), 2*F_15(x) + F_42(x) + F_55(x))
Eq(F_55(x), F_36(x)*F_4(x))
Eq(F_56(x), F_57(x) + F_77(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_2(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_60(x))
Eq(F_63(x), F_57(x) + F_64(x))
Eq(F_64(x), 2*F_15(x) + F_65(x) + F_76(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_67(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_57(x) + F_71(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_70(x))
Eq(F_76(x), F_4(x)*F_63(x))
Eq(F_77(x), 2*F_15(x) + F_78(x) + F_86(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_61(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_80(x))
Eq(F_83(x), F_71(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_83(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_63(x) + F_88(x))
Eq(F_88(x), F_106(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_73(x) + F_92(x))
Eq(F_92(x), F_89(x) + F_93(x))
Eq(F_93(x), F_105(x) + 3*F_15(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_99(x))
Eq(F_96(x), F_71(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_96(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_100(x) + F_89(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_4(x)*F_99(x))
Eq(F_105(x), F_4(x)*F_92(x))
Eq(F_106(x), F_107(x) + 3*F_15(x) + F_94(x))
Eq(F_107(x), F_4(x)*F_88(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_118(x))
Eq(F_110(x), F_111(x) + F_2(x))
Eq(F_111(x), F_112(x) + F_117(x) + F_15(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_11(x) + F_14(x))
Eq(F_115(x), F_116(x) + F_61(x))
Eq(F_116(x), 2*F_15(x) + F_76(x) + F_78(x))
Eq(F_117(x), F_110(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_57(x))
Eq(F_119(x), F_120(x) + 2*F_15(x) + F_65(x))
Eq(F_120(x), F_118(x)*F_4(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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