login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212208 Triangle T(n,k), n>=1, 0<=k<=n^2, read by rows: row n gives the coefficients of the chromatic polynomial of the square diagonal grid graph DG_(n,n), highest powers first. 19
1, 0, 1, -6, 11, -6, 0, 1, -20, 174, -859, 2627, -5082, 6048, -4023, 1134, 0, 1, -42, 825, -10054, 85011, -528254, 2491825, -9084089, 25795983, -57031153, 97292827, -125639547, 118705077, -77301243, 30931875, -5709042, 0, 1, -72, 2492, -55183, 877812 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The square diagonal grid graph DG_(n,n) has n^2 = A000290(n) vertices and 2*(n-1)*(2*n-1) = A002943(n-1) edges. The chromatic polynomial of DG_(n,n) has n^2+1 = A002522(n) coefficients.

LINKS

Alois P. Heinz, Rows n = 1..7, flattened

Wikipedia, Chromatic Polynomial

EXAMPLE

3 example graphs:                          o---o---o

.                                          |\ /|\ /|

.                                          | X | X |

.                                          |/ \|/ \|

.                             o---o        o---o---o

.                             |\ /|        |\ /|\ /|

.                             | X |        | X | X |

.                             |/ \|        |/ \|/ \|

.                o            o---o        o---o---o

Graph:        DG_(1,1)       DG_(2,2)       DG_(3,3)

Vertices:        1              4              9

Edges:           0              6             20

The square diagonal grid graph DG_(2,2) equals the complete graph K_4 and has chromatic polynomial q*(q-1)*(q-2)*(q-3) = q^4 -6*q^3 +11*q^2 -6*q => row 2 = [1, -6, 11, -6, 0].

Triangle T(n,k) begins:

1,    0;

1,   -6,    11,      -6,        0;

1,  -20,   174,    -859,     2627,      -5082, ...

1,  -42,   825,  -10054,    85011,    -528254, ...

1,  -72,  2492,  -55183,   877812,  -10676360, ...

1, -110,  5895, -205054,  5203946, -102687204, ...

1, -156, 11946, -598491, 22059705, -637802510, ...

CROSSREFS

Columns 1-2 give: A000012, (-1)*A002943(n-1).

Row sums (for n>1) and last elements of rows give: A000004, row lengths give: A002522.

Cf. A000290, A212209.

Sequence in context: A009443 A258054 A106540 * A334280 A134012 A103704

Adjacent sequences:  A212205 A212206 A212207 * A212209 A212210 A212211

KEYWORD

sign,tabf

AUTHOR

Alois P. Heinz, May 04 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)