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A212195
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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 staggered hexagonal square grid graph SH_(k,k).
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14
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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, 4038432, 30847500, 393600, 1050, 8, 0, 0, 6, 743601024, 148046704020, 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 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.
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LINKS
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Table of n, a(n) for n=1..45.
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, 4038432, ...
5, 180, 32940, 30847500, 148046704020, ...
6, 480, 393600, 3312560640, 286170443437440, ...
7, 1050, 2735250, 123791435250, 97337320223288250, ...
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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*A068248, 6*A068249.
Rows n=1-10, 16-18 give: A000007, A000038, A040006, 4*A068283, 5*A068284, 6*A068285, 7*A068286, 8*A068287, 9*A068288, 10*A068289, 16*A068290, 17*A068291, 18*A068292.
Cf. A212163, A212194.
Sequence in context: A114699 A182797 A212163 * A228926 A321414 A268865
Adjacent sequences: A212192 A212193 A212194 * A212196 A212197 A212198
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz, May 03 2012
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STATUS
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approved
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