A159300 Number of n-edge-colorings of the first Blanusa Snark.

0, 0, 0, 0, 355147776, 13295453346240, 25745183823790080, 9551858012597416320, 1228730978590223646720, 75591521652028890364416, 2700989527181949160980480, 63609790553234418963634560, 1077023424029916549069987840, 13953705779848069843322869440, 144870494514684002403020537856

Offset

0,5

Comments

The first 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 +292528*n^23 -2771950*n^22 +21130574*n^21 -133117276*n^20 +706470634*n^19 -3203528850*n^18 +12543744946*n^17 -42748437230*n^16 +127531683624*n^15 -334390244348*n^14 +772424405433*n^13 -1573143663006*n^12 +2822347194555*n^11 -4448140977042*n^10 +6127258124900*n^9 -7317667245560*n^8 +7485899667360*n^7 -6443746655392*n^6 +4545578587072*n^5 -2524167305856*n^4 +1033644121344*n^3 -276852249600*n^2 +36240795648*n: seq(a(n), n=0..15);

Mathematica

A159300[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) + 180086) - 1501600) + 10040128) - 55278392) + 255349274) - 1003130126) + 3384451824) - 9875199256) + 25032737268) - 55259917980) + 106253592069) - 177566589204) + 256598638692) - 317795111232) + 332502896672) - 287311809824) + 197726277632) - 101941701504) + 35068465152) - 6040132608);
Array[A159300, 15, 0] (* Paolo Xausa, Jun 04 2026 *)

Crossrefs

Sequence in context: A189125 A258610 A227933 * A308636 A125623 A069319

Adjacent sequences: A159297 A159298 A159299 * A159301 A159302 A159303

Keyword

nonn,easy,changed

Author

Alois P. Heinz, Apr 09 2009

Status

approved