login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..66.

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

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

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

Sequence in context: A098643 A193474 A241020 * A274710 A028625 A344441

Adjacent sequences:  A277441 A277442 A277443 * A277445 A277446 A277447

KEYWORD

nonn,tabl

AUTHOR

Jeremy Tan, Oct 15 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 11:02 EDT 2022. Contains 357147 sequences. (Running on oeis4.)