A277444 - OEIS

%I #12 Nov 05 2016 13:25:05

%S 0,0,2,0,0,6,0,2,0,12,0,0,42,24,20,0,2,48,420,120,30,0,0,306,2160,

%T 2420,360,42,0,2,600,17532,27600,9750,840,56,0,0,2442,115464,375260,

%U 191760,30702,1680,72,0,2,6048,830100,4810680,4098510,917280,81032,3024,90,0,0,20706,5745120,62813540,85691640,28669662,3406368,187560,5040,110

%N Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices.

%C M_1 is two vertices connected by a triple edge and thus behaves like the path graph P_2 in terms of colorings. M_2 is isomorphic to K_4, the tetrahedral graph.

%H N. L. Biggs, R. M. Damerell and D. A. Sands, <a href="https://dx.doi.org/10.1016%2F0095-8956%2872%2990016-0">Recursive families of graphs</a>, Journal of Combinatorial Theory Series B Volume 12 (1972), 123-131. MR0294172

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Möbius Ladder</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a>

%F A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.

%e Square array A(n,k) begins:

%e 0,    0,    0,      0,       0,        0,          0, ...

%e 2,    0,    2,      0,       2,        0,          2, ...

%e 6,    0,   42,     48,     306,      600,       2442, ...

%e 12,  24,  420,   2160,   17532,   115464,     830100, ...

%e 20, 120, 2420,  27600,  375260,  4810680,   62813540, ...

%e 30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...

%Y Cf. A277443 (colorings of prism graphs), A182406 (square grid graphs).

%Y Columns k=1,2 are A002378 and A052762. Rows n=1,2 are A000004 and A010673.

%K nonn,tabl

%O 1,3

%A _Jeremy Tan_, Oct 15 2016