%I #21 Jan 31 2024 12:37:29
%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 480,7,0,0,6,4034304,30847500,393600,1050,8,0,0,6,739642368,
%U 148039757460,3312560640,2735250,2016,9
%N Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the rhombic hexagonal square grid graph RH_(k,k).
%C 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.
%C A differs from A212195 first at (n,k) = (4,5): A(4,5) = 4034304, A212195(4,5) = 4038432.
%H Andrew Howroyd, <a href="/A212163/b212163.txt">Table of n, a(n) for n = 1..153</a>
%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, 4034304, ...
%e 5, 180, 32940, 30847500, 148039757460, ...
%e 6, 480, 393600, 3312560640, 286169360240640, ...
%e 7, 1050, 2735250, 123791435250, 97337270132408250, ...
%Y Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068246, 6*A068247.
%Y 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.
%Y Cf. A212162, A212195, A208054, A208050.
%K nonn,tabl
%O 1,3
%A _Alois P. Heinz_, May 02 2012