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A159042
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Number of n-colorings of the Meredith graph.
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2
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0, 0, 0, 747053585907744, 1624906810580622279614865504, 3900619871010725907313019804069579280, 111374420910619212411328421717468734145825520, 149224399089818120004921602937262545480007723372800, 22074891513933220909862143569462012287952813955355462784
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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The Meredith graph is a quartic graph and has 70 vertices and 140 edges.
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LINKS
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Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.
Index entries for linear recurrences with constant coefficients, signature (71, -2485, 57155, -971635, 13019909, -143218999, 1329890705, -10639125640, 74473879480, -461738052776, 2560547383576, -12802736917880, 58104729088840, -240719591939480, 914734449370024, -3201570572795084, 10358022441395860, -31074067324187580, 86680293062207460, -225368761961739396, 547324136192795676, -1243918491347262900, 2650087220696342700, -5300174441392685400, 9964327949818248552, -17629195603524593592, 29381992672540989320, -46171702771135840360, 68461490315822108120, -95846086442150951368, 126764178842844806648, -158455223553556008310, 187265264199657100730, -209296471752557936110, 221256270138418389602, -221256270138418389602, 209296471752557936110, -187265264199657100730, 158455223553556008310, -126764178842844806648, 95846086442150951368, -68461490315822108120, 46171702771135840360, -29381992672540989320, 17629195603524593592, -9964327949818248552, 5300174441392685400, -2650087220696342700, 1243918491347262900, -547324136192795676, 225368761961739396, -86680293062207460, 31074067324187580, -10358022441395860, 3201570572795084, -914734449370024, 240719591939480, -58104729088840, 12802736917880, -2560547383576, 461738052776, -74473879480, 10639125640, -1329890705, 143218999, -13019909, 971635, -57155, 2485, -71, 1).
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FORMULA
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a(n) = n^70 -140*n^69 + ... (see Maple program).
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MAPLE
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a:= n-> n^70 -140*n^69 +9730*n^68 -447400*n^67 +15305135*n^66 -415313393*n^65 +9307967445*n^64 -177143229030*n^63 +2921177227525*n^62 -42385147826865*n^61 +547655231251908*n^60 -6362445160967745*n^59 +66986770934977025*n^58 -643352690897566600*n^57 +5667629661727827429*n^56 -46013601683266483989*n^55 +345664837976423128305*n^54 -2411147136807901357850*n^53 +15664284197610372703930*n^52 -95031857192627592823326*n^51 +539650543483530480882752*n^50 -2874305532391337539996485*n^49
+14385257377566268242112295*n^48 -67758324543540665508726310*n^47 +300803696795762585094442995*n^46 -1260150898704315083355251212*n^45 +4987235543866672796249231805*n^44 -18664491212756813908060275395*n^43 +66108845581038195328899028504*n^42 -221773640361316596303337110160*n^41 +705086354028668042504214018607*n^40 -2125642553250579162207215767515*n^39 +6079224924265710043776161884405*n^38 -16499617656675529846687195597390*n^37 +42509867076774336819454956263250*n^36
-103988317142611589963712639983561*n^35 +241554032858481141729373679458650*n^34 -532847530987458664066131405620215*n^33 +1116202306596128429166204239670647*n^32 -2220214951406392311415783145265329*n^31 +4192648006602621467299484454778591*n^30 -7514842484274869921819667009399380*n^29 +12780653134533109958801979273097025*n^28 -20616591776665541139098418720204795*n^27 +31528536279800783513205673609584534*n^26 -45684332572157988296327146880432095*n^25 +62678471299025314973514488100228920*n^24
-81362005670284446245879146132398065*n^23 +99836520077262877270258946727344514*n^22 -115684440640637678201229486643623485*n^21 +126433743339285214903926502952473218*n^20 -130154178150874560458698914463229340*n^19 +125999609712703619169371290023059680*n^18 -114495785432462147983155197360247705*n^17 +97447468246116398716460589448822380*n^16 -77479744020570827477339249735141209*n^15 +57371706327812630305881125360391745*n^14 -39416270714623217330027913795782240*n^13
+25011535455740119736457286079204103*n^12 -14576354728913589772989968300121395*n^11 +7747341664555046958454964994697203*n^10 -3722187024914996630144695521734710*n^9 +1598229334625422734646185658775215*n^8 -604231638465790590641296302523484*n^7 +197153623811266041335220568907745*n^6 -53996098994334893792266856899050*n^5 +11917235505602835293961310038870*n^4 -1986603675193265823756221623185*n^3 +222218302960934882569425611786*n^2 -12499044249708706934521437824*n: seq(a(n), n=0..15);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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