%I #25 Jan 22 2022 18:12:57
%S 1,0,2,0,2,3,0,2,18,4,0,2,246,84,5,0,2,7812,9612,260,6,0,2,580986,
%T 6000732,142820,630,7,0,2,101596896,20442892764,828850160,1166910,
%U 1302,8,0,2,41869995708,380053267505964,50820390410180,38128724910,6464682,2408,9
%N Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the square grid graph G_(k,k).
%C The square grid graph G_(n,n) has n^2 = A000290(n) vertices and 2*n*(n-1) = A046092(n-1) edges. The chromatic polynomial of G_(n,n) has n^2+1 = A002522(n) coefficients.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</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, 2, 2, 2, 2, ...
%e 3, 18, 246, 7812, 580986, ...
%e 4, 84, 9612, 6000732, 20442892764, ...
%e 5, 260, 142820, 828850160, 50820390410180, ...
%e 6, 630, 1166910, 38128724910, 21977869327169310, ...
%Y Columns k=1-7 give: A000027, A091940, A068239*2, A068240*2, A068241*2, A068242*2, A068243*2.
%Y Rows n=1-20 give: A000007, A007395, A068253*3, A068254*4, A068255*5, A068256*6, A068257*7, A068258*8, A068259*9, A068260*10, A068261*11, A068262*12, A068263*13, A068264*14, A068265*15, A068266*16, A068267*17, A068268*18, A068269*19, A068270*20.
%Y Cf. A182368.
%K nonn,tabl
%O 1,3
%A _Alois P. Heinz_, Apr 27 2012