A159448 Number of n-edge-colorings of the second Blanusa Snark.

0, 0, 0, 0, 342675456, 13153078605120, 25637821631078400, 9533380086713683200, 1227485144606805073920, 75547606881603808336896, 2700027498853281914634240, 63595142713108801675900800, 1076856076493029796330188800, 13952190527320266709190514240, 144859172135340617188770471936

Offset

0,5

Comments

The second Blanuša Snark is a cubic graph on 18 vertices and 27 edges with edge chromatic number 4.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg, Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions, New Journal of Physics, Volume 11, February 2009.

Eric Weisstein's World of Mathematics, Blanuša Snarks.

Eric Weisstein's World of Mathematics, Edge Coloring.

Index entries for linear recurrences with constant coefficients, signature (28, -378, 3276, -20475, 98280, -376740, 1184040, -3108105, 6906900, -13123110, 21474180, -30421755, 37442160, -40116600, 37442160, -30421755, 21474180, -13123110, 6906900, -3108105, 1184040, -376740, 98280, -20475, 3276, -378, 28, -1).

Formula

a(n) = n^27 - 54*n^26 + ... (see Maple program).

Maple

a:= n-> n^27 -54*n^26 +1413*n^25 -23868*n^24 +292526*n^23 -2771853*n^22 +21128307*n^21 -133083282*n^20 +706103282*n^19 -3200482928*n^18 +12523602732*n^17 -42639446348*n^16 +127040507554*n^15 -332524010611*n^14 +766396617378*n^13 -1556509608394*n^12 +2783042514579*n^11 -4368658864218*n^10 +5990173216956*n^9 -7117375900060*n^8 +7240708340968*n^7 -6196441690112*n^6 +4345188866816*n^5 -2398700714304*n^4 +976694192256*n^3 -260203292160*n^2 +33894503424*n: seq(a(n), n=0..16);

Mathematica

A159448[n_] := (n - 3)*(n - 2)*(n - 1)*n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*((n - 48)*n + 1114) - 16650) + 180084) - 1501515) + 10038393) - 55255755) + 255137339) - 1001615231) + 3375866087) - 9835658251) + 24882339705) - 54782535098) + 104981720529) - 174717360912) + 251244212700) - 309412294812) + 321708942912) - 276121723456) + 188705859328) - 96613918656) + 33010561536) - 5649083904);
Array[A159448, 15, 0] (* Paolo Xausa, Jun 04 2026 *)

Crossrefs

Cf. A159300.

Sequence in context: A204337 A113739 A384388 * A316745 A351459 A358705

Adjacent sequences: A159445 A159446 A159447 * A159449 A159450 A159451

Keyword

nonn,easy,changed

Author

Alois P. Heinz, Apr 11 2009

Status

approved