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A212163
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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).
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21
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..153
Wikipedia, Chromatic Polynomial
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EXAMPLE
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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, ...
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, May 02 2012
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STATUS
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approved
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