02341_02431_03241_03412_03421_04231_04312_04321_13402_14302
Counting sequence:
1, 1, 2, 6, 24, 110, 544, 2814, 15014, 81982, 455894, 2573022, 14701354, 84871918, 494316702, 2901059978, 17139336394, 101851923374, 608406199902, 3651110194354, 22001788156210, 133081427189222, 807704347570678, 4917360106158202, 30022165036930698, 183773180635729838, 1127622885663073662, 6934397783301056770, 42731366510247561954, 263824647059599069574, 1631767403417108951814, 10109384568340727836234, 62729071246726359088090, 389806433720715603160158, 2425644833897932329065838, 15113631742148392087327378, 94284902341556014933816850, 588868133361715365125620214, 3681880926072536273923978838, 23044777003175577310852255450, 144378836234286920372919379466, 905402482249504431366604747854, 5682864878739801813357413075134, 35699510062198123315151142313378, 224444768335622620603114016499522, 1412190201972625298892619316422118, 8891982356014798595843457306523942, 56028868212814763851004223148289130, 353280777686400836323157874709894202, 2229004312186824174560207630375785534, 14072560730489362668118100304584882446, 88898807148911691278014610490609440690, 561913152555701557453262540645872882290, 3553721455192192211418479371668693869526, 22486894846022141484878300240768343429366, 142363613485986772828008487804344244636666, 901745276839335347189426687068581503951722, 5714476978830263973332514818618011525379630, 36230106611222903361160819973414370360300894, 229803371365191974898403321813071289279738306, 1458244443490826325093225139997500878002944674, 9257319002387263969250957155580535612380290246, 58791590502139037283567780125440741704433891526, 373520694157413509928897826085196526374573284746, 2373986626736931308627852752478016218542776350618, 15093880965399794206646279786201720515963919829278, 96001444929734001820902616598134244615545237978542, 610807242814244101197022362277895300195190793050066, 3887547559874979373280311238950956110909774170657234, 24750737479067609240107725849761071883060483274699958, 157629468068548351649369393868493904822652573376042646, 1004198647700696867386416046957924562775615011674583322, 6399279684118682467305597858140789935011792248340209866, 40791363609745247043876239412520347080931260950626347278, 260092367835309019826967535076547414122588174552195280382, 1658845597807087842621435014520688175872947632680415961570, 10582789085541016367148934963005919119486846189007071755266, 67531610834327479491144615259910735976492006721299008962470, 431046337208679991435760938986526337080059758589678971074150, 2751996589059246261679645154363124094718435843758924644391594, 17574226203305357382104795218582925225731747462905112818965242, 112255163812936203137313993632989508104301446486817538515476990, 717192503087435879818019625843697187171555523447713281740495438, 4583128611465062924887264203457644085582895369030474169285727218, 29294286017834041043924027833011345377734138217663002254605301042, 187282035903074374064530610401287799571909131641038216507443644822, 1197566111150252297588118492071444015522560471795948396879983471670, 7659333160887525010620360039502697723122824723044566238881154260538, 48996887988981456733311516814495074780679672468146016874928746177066, 313494670189242995516379296793367646231240103758455626349819556741102, 2006199301838698095234879106203402368851685412772235779409512899614366, 12840987380195485925951784805942519918699702530659843320622070756602370, 82205606213787497915923004097810482068004343119849000254323174610516322, 526358239252843652997567048237599098109258373074163090066337300565171846, 3370829144198919834561000636820722422971323918362571242649415798040906758, 21590653433150002477466155908404481939893604879135305788082249197360283594, 138314279812030691347531905556464559354272872765202779867384920216068682330, 886214689636043448447668581689319181628024391344091637826577559913733902046, 5679107773645314133564763850432943927068277585990814797660551052839052785390, 36398971458878200202938911664469862281898883731741123781483720441026199207954, 233326778550902662332384333241251034667850929560857336975894320190269696509074
Implicit equation for the generating function in Maple syntax:
2*x^3*(x-1)*F(x)^5-2*x^2*(x^2-3*x+1)*F(x)^4-(x-1)*(2*x^2+1)*F(x)^3+(-x^2+4*x-5)*F(x)^2+(-4*x+8)*F(x)-4 = 0
Implicit equation for the generating function in latex syntax:
2 x^{3} \left(x -1\right) F \! \left(x \right)^{5}-2 x^{2} \left(x^{2}-3 x +1\right) F \! \left(x \right)^{4}-\left(x -1\right) \left(2 x^{2}+1\right) F \! \left(x \right)^{3}+\left(-x^{2}+4 x -5\right) F \! \left(x \right)^{2}+\left(-4 x +8\right) F \! \left(x \right)-4 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(6) = 544
a(7) = 2814
a(8) = 15014
a(9) = 81982
a(10) = 455894
a(11) = 2573022
a(12) = 14701354
a(13) = 84871918
a(14) = 494316702
a(15) = 2901059978
a(16) = 17139336394
a(17) = 101851923374
a(18) = 608406199902
a(19) = 3651110194354
a(20) = 22001788156210
a(21) = 133081427189222
a(22) = 807704347570678
a(23) = 4917360106158202
a(24) = 30022165036930698
a(25) = 183773180635729838
a(26) = 1127622885663073662
a(27) = 6934397783301056770
a(28) = 42731366510247561954
a(29) = 263824647059599069574
a(30) = 1631767403417108951814
a(31) = 10109384568340727836234
a(32) = 62729071246726359088090
a(33) = 389806433720715603160158
a(34) = 2425644833897932329065838
a(35) = 15113631742148392087327378
a(36) = 94284902341556014933816850
a(37) = 588868133361715365125620214
a(38) = 3681880926072536273923978838
a(39) = 23044777003175577310852255450
a(40) = 144378836234286920372919379466
a(41) = 905402482249504431366604747854
a(42) = 5682864878739801813357413075134
a(43) = 35699510062198123315151142313378
a(44) = 224444768335622620603114016499522
a(45) = 1412190201972625298892619316422118
a(46) = 8891982356014798595843457306523942
a(47) = 56028868212814763851004223148289130
a(48) = 353280777686400836323157874709894202
a(49) = 2229004312186824174560207630375785534
a(50) = 14072560730489362668118100304584882446
a(51) = 88898807148911691278014610490609440690
a(52) = 561913152555701557453262540645872882290
a(n+53) = -684571623424/3125*n*(n+3)*(n+2)*(n+1)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n)+671744/3125*(31367421*n+123968152)*(n+3)*(n+2)*(n+1)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+1)-1/125*(142325*n^3+21853936*n^2+1118300001*n+19070710440)/(n+54)/(n+53)/(2*n+109)*a(n+51)+1/25*(1929*n^2+201704*n+5269890)/(2*n+109)/(n+54)*a(n+52)-256/3125*(61750953173387*n^4+1301222274794262*n^3+10203378066585886*n^2+35242192236622737*n+45184497177052260)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+4)+128/3125*(616254820865543*n^4+15407217124459762*n^3+143794240050268804*n^2+593186574910597037*n+911814806572939032)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+5)-64/3125*(5163068112875357*n^4+150241148039818720*n^3+1634273609803891972*n^2+7869990955134689459*n+14146758080334252378)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+6)+32/3125*(37365992537243693*n^4+1242830512620975881*n^3+15460069981490023243*n^2+85194986825310888553*n+175395080679324695166)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+7)-32/3125*(117402168039830971*n^4+4386231178759590298*n^3+61300470875537879831*n^2+379673530848347682362*n+879020130259163162988)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+8)+16/3125*(635004810060654751*n^4+26237347800960043901*n^3+405644950057376848463*n^2+2780569185206532680563*n+7128568563302630455290)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+9)-16/3125*(1457584839532261818*n^4+65741172673748813335*n^3+1109971170358619567397*n^2+8313333085661486372954*n+23301336196500640442304)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+10)+16/3125*(2791609573658189719*n^4+135926787300484940825*n^3+2478803467226213273093*n^2+20063731171557967684621*n+60812053820266078490706)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+11)-4/3125*(17387315312179207913*n^4+904216760661564479254*n^3+17619141743776933058875*n^2+152454422118878431745414*n+494238600179903483492592)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+12)+8/3125*(10404967866607148371*n^4+569509010828303116405*n^3+11678782662230086519943*n^2+106348703077903149567611*n+362855080233445811924778)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+13)-2/3125*(31734775106786906287*n^4+1749743149195419570118*n^3+35934435174524407653821*n^2+325504760453319636351014*n+1096116616313714630269296)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+14)-8/3125*(838820623429852751*n^4+126278325181210458970*n^3+4735899652784662549246*n^2+68245585565829721330145*n+341812200042095939599620)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+15)+8/3125*(15197021134378574734*n^4+1137794634904024824994*n^3+31603043438226398820683*n^2+386588345168371562469713*n+1759454158114665172179726)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+16)-2/3125*(122816098210085221723*n^4+9331194013525163750970*n^3+264715349328901879711121*n^2+3324389778504423981946914*n+15598115908914820999791528)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+17)+1/3125*(327914987019101998473*n^4+25900145704973716726322*n^3+765103798569356068369227*n^2+10019724142748887860867346*n+49087378300489152585413304)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+18)-2/3125*(165752897093945872091*n^4+13715700460522495681992*n^3+424672505418211911169729*n^2+5831693886097097038847976*n+29970107321962481615068668)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+19)+1/3125*(256585241086147242151*n^4+22431522365657882376174*n^3+733361258964664187594057*n^2+10628496827312880516312186*n+57623650222736236150405416)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+20)-1/3125*(138916148957156323235*n^4+13138322919933233564466*n^3+462738040353604669596817*n^2+7199770625025068208817938*n+41784819735652601072732712)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+21)+2/3125*(13091135735209972807*n^4+1675469681624634346676*n^3+73483346020344853504229*n^2+1358092131277667440702012*n+9085525953681097899376680)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+22)+3/3125*(16127260067929406389*n^4+1261675131591453589344*n^3+35525072691960326648999*n^2+417032649976366853527992*n+1637025861533872830863756)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+23)-2/3125*(38680357766949485170*n^4+3547008443995735332491*n^3+121571849398611394919945*n^2+1845861222526589109073546*n+10476500628629104807907664)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+24)+2/3125*(36460078588255178929*n^4+3607194871364283273430*n^3+133952086787361272789945*n^2+2213769220589877048346376*n+13744966601511699330353304)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+25)-3/3125*(17662245910564603639*n^4+1858094828421181480796*n^3+73458289059037160196735*n^2+1293861726344971132584642*n+8569566953290322789331784)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+26)+1/3125*(31060890694619400413*n^4+3450218189966555609198*n^3+144048333851470659083047*n^2+2679525340569402401041750*n+18740162722787580820097616)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+27)-1/3125*(13692380689815037689*n^4+1598182812854991669353*n^3+70106498227344212602356*n^2+1369901408174483498288074*n+10061255759176750190720004)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+28)+1/3125*(2657247316796376487*n^4+330914954087472934202*n^3+15495069199396871421857*n^2+323281082182026261553990*n+2535185828406366901612932)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+29)+1/3125*(2567281240368644117*n^4+310825403480106935975*n^3+14080441633071250524724*n^2+282787007422540666378630*n+2123961497418970923501468)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+30)-1/3125*(3632318161790348001*n^4+460343215828375705892*n^3+21865567223657779338837*n^2+461315648868195487192522*n+3647527456403097207271512)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+31)+1/3125*(2635984997078070559*n^4+345246991732254809294*n^3+16950192676402799382233*n^2+369711114451167232379014*n+3022779010891746206734488)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+32)-3/3125*(433275303191565294*n^4+58530580396848108597*n^3+2963902167476333396343*n^2+66679977317024963127338*n+562332934699306837281848)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+33)+1/3125*(434659762373805766*n^4+60577725387573921843*n^3+3164641890208823461667*n^2+73447406979567317917044*n+638981542784815495281960)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+34)-1/3125*(81308773524044975*n^4+11732948578267950488*n^3+634574440509680145043*n^2+15246376583311549701364*n+137305893064299350601504)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+35)-1/3125*(2529921999586388*n^4+340909442931676659*n^3+17058010578625916803*n^2+374655303055059877764*n+3036535198418514495120)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+36)+1/3125*(6111970606153223*n^4+929020420137259507*n^3+52905638661191203756*n^2+1337828377311062320628*n+12674711750395260810816)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+37)-2/3125*(758227674787723*n^4+122834354133113059*n^3+7439383274185675568*n^2+199698563399698488644*n+2005249905544050300936)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+38)+1/3125*(151868234327591*n^4+29586700413577648*n^3+2085449562096138013*n^2+63707543987369969600*n+716355695245479576300)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+39)-2/3125*(24071763905554*n^4+4770275801595469*n^3+343515615807315443*n^2+10749248066119170290*n+124021258153391319972)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+40)+2/3125*(16911876835548*n^4+3003721221379049*n^3+199535056042934223*n^2+5877315958778532232*n+64782578144726655036)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+41)-1/3125*(9761371151215*n^4+1722657594685938*n^3+114013613547792473*n^2+3353979092367671346*n+37001063980931876832)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+42)+1/3125*(865942916165*n^4+154748455929630*n^3+10387952163979015*n^2+310400141944998282*n+3482976216466678728)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+43)+1/3125*(167951143909*n^4+32015543547505*n^3+2278292332287764*n^2+71775825380327762*n+845084226369332100)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+44)-1/3125*(34827814457*n^4+7347923497500*n^3+571393492775953*n^2+19484569604806230*n+246499427108345940)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+45)-1/3125*(9973721551*n^4+1640039780157*n^3+99109295893364*n^2+2589647814333498*n+24386243883474300)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+46)+1/625*(1070463895*n^4+198852761428*n^3+13837735335239*n^2+427491617969810*n+4946512402382856)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+47)-1/625*(178351355*n^4+34501608694*n^3+2502525293461*n^2+80664143069870*n+974899608407520)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+48)+3/625*(212330*n^4+51824907*n^3+4595697593*n^2+177057695390*n+2514697155600)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+49)+3/625*(1475307*n^4+296729439*n^3+22375510328*n^2+749726661246*n+9418065561000)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+50)+512/3125*(n+3)*(4911330196364*n^3+70341931089269*n^2+333734115676060*n+523804197516352)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+3)-2048/3125*(n+3)*(n+2)*(141907162472*n^2+1229372938639*n+2648266363268)/(n+54)/(n+53)/(n+52)/(2*n+109)*a(n+2), n >= 53
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) = 24
a \! \left(5\right) = 110
a \! \left(6\right) = 544
a \! \left(7\right) = 2814
a \! \left(8\right) = 15014
a \! \left(9\right) = 81982
a \! \left(10\right) = 455894
a \! \left(11\right) = 2573022
a \! \left(12\right) = 14701354
a \! \left(13\right) = 84871918
a \! \left(14\right) = 494316702
a \! \left(15\right) = 2901059978
a \! \left(16\right) = 17139336394
a \! \left(17\right) = 101851923374
a \! \left(18\right) = 608406199902
a \! \left(19\right) = 3651110194354
a \! \left(20\right) = 22001788156210
a \! \left(21\right) = 133081427189222
a \! \left(22\right) = 807704347570678
a \! \left(23\right) = 4917360106158202
a \! \left(24\right) = 30022165036930698
a \! \left(25\right) = 183773180635729838
a \! \left(26\right) = 1127622885663073662
a \! \left(27\right) = 6934397783301056770
a \! \left(28\right) = 42731366510247561954
a \! \left(29\right) = 263824647059599069574
a \! \left(30\right) = 1631767403417108951814
a \! \left(31\right) = 10109384568340727836234
a \! \left(32\right) = 62729071246726359088090
a \! \left(33\right) = 389806433720715603160158
a \! \left(34\right) = 2425644833897932329065838
a \! \left(35\right) = 15113631742148392087327378
a \! \left(36\right) = 94284902341556014933816850
a \! \left(37\right) = 588868133361715365125620214
a \! \left(38\right) = 3681880926072536273923978838
a \! \left(39\right) = 23044777003175577310852255450
a \! \left(40\right) = 144378836234286920372919379466
a \! \left(41\right) = 905402482249504431366604747854
a \! \left(42\right) = 5682864878739801813357413075134
a \! \left(43\right) = 35699510062198123315151142313378
a \! \left(44\right) = 224444768335622620603114016499522
a \! \left(45\right) = 1412190201972625298892619316422118
a \! \left(46\right) = 8891982356014798595843457306523942
a \! \left(47\right) = 56028868212814763851004223148289130
a \! \left(48\right) = 353280777686400836323157874709894202
a \! \left(49\right) = 2229004312186824174560207630375785534
a \! \left(50\right) = 14072560730489362668118100304584882446
a \! \left(51\right) = 88898807148911691278014610490609440690
a \! \left(52\right) = 561913152555701557453262540645872882290
a \! \left(n +53\right) = -\frac{684571623424 n \left(n +3\right) \left(n +2\right) \left(n +1\right) a \! \left(n \right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{671744 \left(31367421 n +123968152\right) \left(n +3\right) \left(n +2\right) \left(n +1\right) a \! \left(n +1\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(142325 n^{3}+21853936 n^{2}+1118300001 n +19070710440\right) a \! \left(n +51\right)}{125 \left(n +54\right) \left(n +53\right) \left(2 n +109\right)}+\frac{\left(1929 n^{2}+201704 n +5269890\right) a \! \left(n +52\right)}{25 \left(2 n +109\right) \left(n +54\right)}-\frac{256 \left(61750953173387 n^{4}+1301222274794262 n^{3}+10203378066585886 n^{2}+35242192236622737 n +45184497177052260\right) a \! \left(n +4\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{128 \left(616254820865543 n^{4}+15407217124459762 n^{3}+143794240050268804 n^{2}+593186574910597037 n +911814806572939032\right) a \! \left(n +5\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{64 \left(5163068112875357 n^{4}+150241148039818720 n^{3}+1634273609803891972 n^{2}+7869990955134689459 n +14146758080334252378\right) a \! \left(n +6\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{32 \left(37365992537243693 n^{4}+1242830512620975881 n^{3}+15460069981490023243 n^{2}+85194986825310888553 n +175395080679324695166\right) a \! \left(n +7\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{32 \left(117402168039830971 n^{4}+4386231178759590298 n^{3}+61300470875537879831 n^{2}+379673530848347682362 n +879020130259163162988\right) a \! \left(n +8\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{16 \left(635004810060654751 n^{4}+26237347800960043901 n^{3}+405644950057376848463 n^{2}+2780569185206532680563 n +7128568563302630455290\right) a \! \left(n +9\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{16 \left(1457584839532261818 n^{4}+65741172673748813335 n^{3}+1109971170358619567397 n^{2}+8313333085661486372954 n +23301336196500640442304\right) a \! \left(n +10\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{16 \left(2791609573658189719 n^{4}+135926787300484940825 n^{3}+2478803467226213273093 n^{2}+20063731171557967684621 n +60812053820266078490706\right) a \! \left(n +11\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{4 \left(17387315312179207913 n^{4}+904216760661564479254 n^{3}+17619141743776933058875 n^{2}+152454422118878431745414 n +494238600179903483492592\right) a \! \left(n +12\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{8 \left(10404967866607148371 n^{4}+569509010828303116405 n^{3}+11678782662230086519943 n^{2}+106348703077903149567611 n +362855080233445811924778\right) a \! \left(n +13\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(31734775106786906287 n^{4}+1749743149195419570118 n^{3}+35934435174524407653821 n^{2}+325504760453319636351014 n +1096116616313714630269296\right) a \! \left(n +14\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{8 \left(838820623429852751 n^{4}+126278325181210458970 n^{3}+4735899652784662549246 n^{2}+68245585565829721330145 n +341812200042095939599620\right) a \! \left(n +15\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{8 \left(15197021134378574734 n^{4}+1137794634904024824994 n^{3}+31603043438226398820683 n^{2}+386588345168371562469713 n +1759454158114665172179726\right) a \! \left(n +16\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(122816098210085221723 n^{4}+9331194013525163750970 n^{3}+264715349328901879711121 n^{2}+3324389778504423981946914 n +15598115908914820999791528\right) a \! \left(n +17\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(327914987019101998473 n^{4}+25900145704973716726322 n^{3}+765103798569356068369227 n^{2}+10019724142748887860867346 n +49087378300489152585413304\right) a \! \left(n +18\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(165752897093945872091 n^{4}+13715700460522495681992 n^{3}+424672505418211911169729 n^{2}+5831693886097097038847976 n +29970107321962481615068668\right) a \! \left(n +19\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(256585241086147242151 n^{4}+22431522365657882376174 n^{3}+733361258964664187594057 n^{2}+10628496827312880516312186 n +57623650222736236150405416\right) a \! \left(n +20\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(138916148957156323235 n^{4}+13138322919933233564466 n^{3}+462738040353604669596817 n^{2}+7199770625025068208817938 n +41784819735652601072732712\right) a \! \left(n +21\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{2 \left(13091135735209972807 n^{4}+1675469681624634346676 n^{3}+73483346020344853504229 n^{2}+1358092131277667440702012 n +9085525953681097899376680\right) a \! \left(n +22\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{3 \left(16127260067929406389 n^{4}+1261675131591453589344 n^{3}+35525072691960326648999 n^{2}+417032649976366853527992 n +1637025861533872830863756\right) a \! \left(n +23\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(38680357766949485170 n^{4}+3547008443995735332491 n^{3}+121571849398611394919945 n^{2}+1845861222526589109073546 n +10476500628629104807907664\right) a \! \left(n +24\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{2 \left(36460078588255178929 n^{4}+3607194871364283273430 n^{3}+133952086787361272789945 n^{2}+2213769220589877048346376 n +13744966601511699330353304\right) a \! \left(n +25\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{3 \left(17662245910564603639 n^{4}+1858094828421181480796 n^{3}+73458289059037160196735 n^{2}+1293861726344971132584642 n +8569566953290322789331784\right) a \! \left(n +26\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(31060890694619400413 n^{4}+3450218189966555609198 n^{3}+144048333851470659083047 n^{2}+2679525340569402401041750 n +18740162722787580820097616\right) a \! \left(n +27\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(13692380689815037689 n^{4}+1598182812854991669353 n^{3}+70106498227344212602356 n^{2}+1369901408174483498288074 n +10061255759176750190720004\right) a \! \left(n +28\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(2657247316796376487 n^{4}+330914954087472934202 n^{3}+15495069199396871421857 n^{2}+323281082182026261553990 n +2535185828406366901612932\right) a \! \left(n +29\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(2567281240368644117 n^{4}+310825403480106935975 n^{3}+14080441633071250524724 n^{2}+282787007422540666378630 n +2123961497418970923501468\right) a \! \left(n +30\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(3632318161790348001 n^{4}+460343215828375705892 n^{3}+21865567223657779338837 n^{2}+461315648868195487192522 n +3647527456403097207271512\right) a \! \left(n +31\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(2635984997078070559 n^{4}+345246991732254809294 n^{3}+16950192676402799382233 n^{2}+369711114451167232379014 n +3022779010891746206734488\right) a \! \left(n +32\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{3 \left(433275303191565294 n^{4}+58530580396848108597 n^{3}+2963902167476333396343 n^{2}+66679977317024963127338 n +562332934699306837281848\right) a \! \left(n +33\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(434659762373805766 n^{4}+60577725387573921843 n^{3}+3164641890208823461667 n^{2}+73447406979567317917044 n +638981542784815495281960\right) a \! \left(n +34\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(81308773524044975 n^{4}+11732948578267950488 n^{3}+634574440509680145043 n^{2}+15246376583311549701364 n +137305893064299350601504\right) a \! \left(n +35\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(2529921999586388 n^{4}+340909442931676659 n^{3}+17058010578625916803 n^{2}+374655303055059877764 n +3036535198418514495120\right) a \! \left(n +36\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(6111970606153223 n^{4}+929020420137259507 n^{3}+52905638661191203756 n^{2}+1337828377311062320628 n +12674711750395260810816\right) a \! \left(n +37\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(758227674787723 n^{4}+122834354133113059 n^{3}+7439383274185675568 n^{2}+199698563399698488644 n +2005249905544050300936\right) a \! \left(n +38\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(151868234327591 n^{4}+29586700413577648 n^{3}+2085449562096138013 n^{2}+63707543987369969600 n +716355695245479576300\right) a \! \left(n +39\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2 \left(24071763905554 n^{4}+4770275801595469 n^{3}+343515615807315443 n^{2}+10749248066119170290 n +124021258153391319972\right) a \! \left(n +40\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{2 \left(16911876835548 n^{4}+3003721221379049 n^{3}+199535056042934223 n^{2}+5877315958778532232 n +64782578144726655036\right) a \! \left(n +41\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(9761371151215 n^{4}+1722657594685938 n^{3}+114013613547792473 n^{2}+3353979092367671346 n +37001063980931876832\right) a \! \left(n +42\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(865942916165 n^{4}+154748455929630 n^{3}+10387952163979015 n^{2}+310400141944998282 n +3482976216466678728\right) a \! \left(n +43\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(167951143909 n^{4}+32015543547505 n^{3}+2278292332287764 n^{2}+71775825380327762 n +845084226369332100\right) a \! \left(n +44\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(34827814457 n^{4}+7347923497500 n^{3}+571393492775953 n^{2}+19484569604806230 n +246499427108345940\right) a \! \left(n +45\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(9973721551 n^{4}+1640039780157 n^{3}+99109295893364 n^{2}+2589647814333498 n +24386243883474300\right) a \! \left(n +46\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{\left(1070463895 n^{4}+198852761428 n^{3}+13837735335239 n^{2}+427491617969810 n +4946512402382856\right) a \! \left(n +47\right)}{625 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{\left(178351355 n^{4}+34501608694 n^{3}+2502525293461 n^{2}+80664143069870 n +974899608407520\right) a \! \left(n +48\right)}{625 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{3 \left(212330 n^{4}+51824907 n^{3}+4595697593 n^{2}+177057695390 n +2514697155600\right) a \! \left(n +49\right)}{625 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{3 \left(1475307 n^{4}+296729439 n^{3}+22375510328 n^{2}+749726661246 n +9418065561000\right) a \! \left(n +50\right)}{625 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}+\frac{512 \left(n +3\right) \left(4911330196364 n^{3}+70341931089269 n^{2}+333734115676060 n +523804197516352\right) a \! \left(n +3\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}-\frac{2048 \left(n +3\right) \left(n +2\right) \left(141907162472 n^{2}+1229372938639 n +2648266363268\right) a \! \left(n +2\right)}{3125 \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(2 n +109\right)}, \quad n \geq 53
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24233/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[23,x]
F[11,x] = 1/F[23,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[53,x]
F[14,x] = -F[50,x]+F[15,x]
F[15,x] = F[16,x]+F[46,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[23,x]
F[19,x] = F[20,x]+F[44,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[26,x]
F[26,x] = 1/F[23,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[2,x]*F[21,x]
F[30,x] = F[31,x]
F[31,x] = F[16,x]*F[23,x]*F[32,x]
F[32,x] = F[33,x]+F[39,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[32,x]
F[37,x] = F[38,x]
F[38,x] = F[23,x]*F[34,x]
F[39,x] = -F[43,x]+F[40,x]
F[40,x] = 1/F[23,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[0,x]+F[21,x]
F[43,x] = F[21,x]+F[33,x]
F[44,x] = F[45,x]
F[45,x] = F[16,x]*F[21,x]*F[23,x]
F[46,x] = F[47,x]
F[47,x] = F[16,x]*F[23,x]*F[48,x]
F[48,x] = F[4,x]+F[49,x]
F[49,x] = F[0,x]*F[2,x]
F[50,x] = F[0,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[0,x]*F[23,x]*F[48,x]
F[53,x] = F[54,x]
F[54,x] = F[21,x]*F[23,x]*F[55,x]
F[55,x] = -F[50,x]+F[8,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{53}\! \left(x \right)
F_{14}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{44}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right) F_{21}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{23}\! \left(x \right) F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)+F_{33}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = F_{0}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right) F_{23}\! \left(x \right) F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{8}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_23(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_53(x))
Eq(F_14(x), F_15(x) - F_50(x))
Eq(F_15(x), F_16(x) + F_46(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_23(x))
Eq(F_19(x), F_20(x) + F_44(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_26(x))
Eq(F_26(x), F_27(x)/F_23(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_2(x)*F_21(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_16(x)*F_23(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_39(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_32(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_23(x)*F_34(x))
Eq(F_39(x), F_40(x) - F_43(x))
Eq(F_40(x), F_41(x)/F_23(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_0(x) + F_21(x))
Eq(F_43(x), F_21(x) + F_33(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_16(x)*F_21(x)*F_23(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_16(x)*F_23(x)*F_48(x))
Eq(F_48(x), F_4(x) + F_49(x))
Eq(F_49(x), F_0(x)*F_2(x))
Eq(F_50(x), F_0(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_0(x)*F_23(x)*F_48(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_21(x)*F_23(x)*F_55(x))
Eq(F_55(x), -F_50(x) + F_8(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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 2], [0, 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