A158726 Number of n-colorings of Tutte's graph.

0, 0, 0, 5031109632, 12269254183718467176, 30260924995437351313959360, 2196937758510267974836823961240, 18289382049683531604887056007569920, 35121324556313091408295530293937599472

Offset: 0

Author

Alois P. Heinz, Mar 24 2009

Keywords

• nonn
• easy

Comments

Tutte's graph is a non-Hamiltonian 3-connected cubic graph and has 46 vertices and 69 edges.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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.
• Eric Weisstein's World of Mathematics, Tutte's Graph
• Eric Weisstein's World of Mathematics, Chromatic Polynomial
• Index entries for linear recurrences with constant coefficients, signature (47, -1081, 16215, -178365, 1533939, -10737573, 62891499, -314457495, 1362649145, -5178066751, 17417133617, -52251400851, 140676848445, -341643774795, 751616304549, -1503232609098, 2741188875414, -4568648125690, 6973199770790, -9762479679106, 12551759587422, -14833897694226, 16123801841550, -16123801841550, 14833897694226, -12551759587422, 9762479679106, -6973199770790, 4568648125690, -2741188875414, 1503232609098, -751616304549, 341643774795, -140676848445, 52251400851, -17417133617, 5178066751, -1362649145, 314457495, -62891499, 10737573, -1533939, 178365, -16215, 1081, -47, 1).

Programs

Maple

a:= n-> n^46 -69*n^45 +2346*n^44 -52388*n^43 +864090*n^42 -11224668*n^41 [phone]*n^40 -1073918754*n^39 [phone]*n^38 -56003778409*n^37 [phone]*n^36 -1779060044140*n^35 [phone]*n^34 -36919189414713*n^33 [phone]*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
+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 [phone]*n^2 -53976523441418*n: seq(a(n), n=0..15);

Formula

a(n) = n^46 -69*n^45 + ... (see Maple program).