A068284 -id:A068284

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A212195

Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the staggered hexagonal square grid graph SH_(k,k).

+10
14

1, 0, 2, 0, 0, 3, 0, 0, 6, 4, 0, 0, 6, 48, 5, 0, 0, 6, 1056, 180, 6, 0, 0, 6, 45696, 32940, 480, 7, 0, 0, 6, 4038432, 30847500, 393600, 1050, 8, 0, 0, 6, 743601024, 148046704020, 3312560640, 2735250, 2016, 9

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OFFSET

1,3

COMMENTS

The staggered hexagonal square grid graph SH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212194 for example. The chromatic polynomial of SH_(n,n) has n^2+1 = A002522(n) coefficients.

A differs from A212163 first at (n,k) = (4,5): A(4,5) = 4038432, A212163(4,5) = 4034304.

LINKS

Table of n, a(n) for n=1..45.

Wikipedia, Chromatic Polynomial

EXAMPLE

Square array A(n,k) begins:

1, 0, 0, 0, 0, ...

2, 0, 0, 0, 0, ...

3, 6, 6, 6, 6, ...

4, 48, 1056, 45696, 4038432, ...

5, 180, 32940, 30847500, 148046704020, ...

6, 480, 393600, 3312560640, 286170443437440, ...