Search: id:A158726
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%I A158726
%S A158726 0,0,0,5031109632,12269254183718467176,30260924995437351313959360,
%T A158726 2196937758510267974836823961240,18289382049683531604887056007569920,
%U A158726 35121324556313091408295530293937599472
%N A158726 Number of n-colorings of Tutte's graph.
%C A158726 Tutte's graph is a non-Hamiltonian 3-connected cubic graph and has 46 
               vertices and 69 edges.
%H A158726 Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/TuttesGraph.html">
               Tutte's Graph</a>".
%H A158726 Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">
               Chromatic Polynomial</a>".
%H A158726 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: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/
               023001">10.1088/1367-2630/11/2/023001</a>.
%F A158726 a(n) = n^46 -69*n^45 + ... (see Maple program).
%p A158726 a:= n-> n^46 -69*n^45 +2346*n^44 -52388*n^43 +864090*n^42 -11224668*n^41 
               +119571727*n^40 -1073918754*n^39 +8297710913*n^38 -56003778409*n^37 
               +334132896213*n^36 -1779060044140*n^35 +8518879333839*n^34 -36919189414713*n^33 
               +145576288126673*n^32 -524582778909860*n^31 +1733926880890968*n^30 
               -5273413882507148*n^29 +14795464456226603*n^28 -38377923819676665*n^27 
               +92198081030378865*n^26 -205432211375233863*n^25 +425010309538429644*n^24 
               -817071784257131829*n^23 +1460390102714891125*n^22 -2427269661879319776*n^21
%p A158726 +3751228994738590035*n^20 -5388532329671500274*n^19 +7189601527638524235*n^18 
               -8900642446016426022*n^17 +10209296517904329101*n^16 -10829536267918267572*n^15 
               +10597816407206520989*n^14 -9538751939522734322*n^13 +7866252277444668060*n^12 
               -5914803096515435788*n^11 +4030254107398817420*n^10 -2468895384899966394*n^9 
               +1345725960500827472*n^8 -643733683706244378*n^7 +265193759121824448*n^6 
               -91607610668166096*n^5 +25500157237142048*n^4 -5365394930683662*n^3 
               +758432173511393*n^2 -53976523441418*n: seq (a(n), n=0..15);
%Y A158726 Sequence in context: A050259 A015384 A072018 this_sequence A017409 A017529 
               A133688
%Y A158726 Adjacent sequences: A158723 A158724 A158725 this_sequence A158727 A158728 
               A158729
%K A158726 nonn
%O A158726 0,4
%A A158726 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 24 2009

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