A159447 Number of n-edge-colorings of the second Celmins-Swart Snark.

0, 0, 0, 0, 2258870796288, 9047768830231276800, 506336252436007271792640, 2604852575650929700554897600, 2901541315803996724909094338560, 1113635084163037955678982524179968, 194993996964612517111634963280691200, 18697739035489738337034253081138308480

Offset

0,5

Comments

The second Celmins-Swart Snark is a cubic graph on 26 vertices and 39 edges with edge chromatic number 4.

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, Celmins-Swart Snarks.

Eric Weisstein's World of Mathematics, Edge Coloring.

Index entries for linear recurrences with constant coefficients, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).

Formula

a(n) = n^39 -78*n^38 + ... (see Maple program).

Maple

a:= n-> n^39 -78*n^38 +2977*n^37 -74100*n^36 +1352640*n^35 -19306594*n^34 +224342277*n^33 -2181791404*n^32 +18118893123*n^31 -130452836327*n^30 +823952578392*n^29 -4608389780429*n^28 +22997509515589*n^27 -103033396258400*n^26 +416525331736816*n^25 -1525737772270530*n^24 +5081295004914867*n^23 -15428507680657788*n^22 +42803369770538734*n^21 -108682235921838363*n^20 +252855988591085175*n^19 -539410912179380029*n^18 +1055315901598357898*n^17 -1892867854923086364*n^16 +3109878686211564875*n^15 -4672808797433106398*n^14 +6406393723078014052*n^13 -7987839935998545020*n^12 +9017573199563822008*n^11 -9162177613893661616*n^10 +8311775652268340640*n^9 -6661120231484154048*n^8 +4648572768670421376*n^7 -2769843755431745280*n^6 +1370525684357079552*n^5 -540501319873105920*n^4 +159143872899272704*n^3 -31049988392951808*n^2 +3004158272716800*n: seq(a(n), n=0..12);

Crossrefs

Cf. A159304.

Sequence in context: A234073 A026081 A159304 * A172598 A321708 A077304

Adjacent sequences: A159444 A159445 A159446 * A159448 A159449 A159450

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 11 2009

Status

approved