A277444 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.
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, 2420, 360, 42, 0, 2, 600, 17532, 27600, 9750, 840, 56, 0, 0, 2442, 115464, 375260, 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
Offset: 1
Examples
Square array A(n,k) begins: 0, 0, 0, 0, 0, 0, 0, ... 2, 0, 2, 0, 2, 0, 2, ... 6, 0, 42, 48, 306, 600, 2442, ... 12, 24, 420, 2160, 17532, 115464, 830100, ... 20, 120, 2420, 27600, 375260, 4810680, 62813540, ... 30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...
Links
- N. L. Biggs, R. M. Damerell and D. A. Sands, Recursive families of graphs, Journal of Combinatorial Theory Series B Volume 12 (1972), 123-131. MR0294172
- Eric Weisstein's World of Mathematics, Möbius Ladder
- Wikipedia, Chromatic polynomial
Crossrefs
Formula
A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.
Comments