OFFSET
1,3
COMMENTS
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.
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
FORMULA
A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.
EXAMPLE
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, ...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jeremy Tan, Oct 15 2016
STATUS
approved