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A212163 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the rhombic hexagonal square grid graph RH_(k,k). 21
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, 4034304, 30847500, 393600, 1050, 8, 0, 0, 6, 739642368, 148039757460, 3312560640, 2735250, 2016, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The rhombic hexagonal square grid graph RH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212162 for example. The chromatic polynomial of RH_(n,n) has n^2+1 = A002522(n) coefficients.

A differs from A212195 first at (n,k) = (4,5): A(4,5) = 4034304, A212195(4,5) = 4038432.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..153

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,           4034304, ...

5,  180,   32940,     30847500,      148039757460, ...

6,  480,  393600,   3312560640,   286169360240640, ...

7, 1050, 2735250, 123791435250, 97337270132408250, ...

CROSSREFS

Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068246, 6*A068247.

Rows n=1-15 give: A000007, A000038, A040006, 4*A068271, 5*A068272, 6*A068273, 7*A068274, 8*A068275, 9*A068276, 10*A068277, 11*A068278, 12*A068279, 13*A068280, 14*A068281, 15*A068282.

Cf. A212162, A212195, A208054, A208050.

Sequence in context: A290976 A114699 A182797 * A212195 A228926 A321414

Adjacent sequences:  A212160 A212161 A212162 * A212164 A212165 A212166

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, May 02 2012

STATUS

approved

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Last modified April 23 06:30 EDT 2021. Contains 343199 sequences. (Running on oeis4.)