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%I #17 Jan 28 2019 17:14:04
%S 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,
%T 480,7,0,0,6,4038432,30847500,393600,1050,8,0,0,6,743601024,
%U 148046704020,3312560640,2735250,2016,9
%N 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).
%C 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.
%C A differs from A212163 first at (n,k) = (4,5): A(4,5) = 4038432, A212163(4,5) = 4034304.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a>
%e Square array A(n,k) begins:
%e 1, 0, 0, 0, 0, ...
%e 2, 0, 0, 0, 0, ...
%e 3, 6, 6, 6, 6, ...
%e 4, 48, 1056, 45696, 4038432, ...
%e 5, 180, 32940, 30847500, 148046704020, ...
%e 6, 480, 393600, 3312560640, 286170443437440, ...
%e 7, 1050, 2735250, 123791435250, 97337320223288250, ...
%Y Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068248, 6*A068249.
%Y 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.
%Y Cf. A212163, A212194.
%K nonn,tabl
%O 1,3
%A _Alois P. Heinz_, May 03 2012