A159304 Number of n-edge-colorings of the first Celmins-Swart Snark.

0, 0, 0, 0, 2206891769856, 8985991276142132160, 504931336656614465863680, 2601338329526671167102526080, 2899404097467850319505677352960, 1113148891816725486745876952560896, 194940322566512126706553318999326720, 18694333110162724133404815215312837760

Offset

0,5

Comments

The first 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.

Weisstein, Eric W. "Celmins-Swart Snarks".

Weisstein, Eric W. "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 +1352638*n^35 -19306444*n^34 +224336780*n^33 -2181660236*n^32 +18116601783*n^31 -130421600004*n^30 +823606665410*n^29 -4605191478887*n^28 +22972325860222*n^27 -102861993275074*n^26 +415505355620273*n^25 -1520383108997852*n^24 +5056318428100120*n^23 -15324409097625111*n^22 +42413962546976794*n^21 -107370302818434833*n^20 +248864920263599380*n^19 -528428118736582730*n^18 +1027948527265211882*n^17 -1831097576516314792*n^16 +2983651836264882802*n^15 -4439572435166623979*n^14 +6017557807197304266*n^13 -7404850682465523144*n^12 +8234986403532221984*n^11 -8227285750919442640*n^10 +7325807552609513824*n^9 -5752861850845416448*n^8 +3928127258221483264*n^7 -2287256698390546944*n^6 +1104929871270325248*n^5 -425172902397374464*n^4 +122110240451633152*n^3 -23239128691064832*n^2 +2193821279649792*n: seq(a(n), n=0..13);

Crossrefs

Sequence in context: A032756 A234073 A026081 * A159447 A172598 A321708

Adjacent sequences: A159301 A159302 A159303 * A159305 A159306 A159307

Keyword

nonn

Author

Alois P. Heinz, Apr 09 2009

Status

approved