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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
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
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.
Sequence in context: A290976 A114699 A182797 * A212195 A228926 A372727
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, May 02 2012
STATUS
approved