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A182406 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).

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%I A182406 #26 Feb 16 2025 08:33:13
%S A182406 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 A182406 6000732,142820,630,7,0,2,101596896,20442892764,828850160,1166910,
%U A182406 1302,8,0,2,41869995708,380053267505964,50820390410180,38128724910,6464682,2408,9
%N A182406 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 A182406 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 A182406 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A182406 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a>
%e A182406 Square array A(n,k) begins:
%e A182406   1,   0,       0,           0,                 0, ...
%e A182406   2,   2,       2,           2,                 2, ...
%e A182406   3,  18,     246,        7812,            580986, ...
%e A182406   4,  84,    9612,     6000732,       20442892764, ...
%e A182406   5, 260,  142820,   828850160,    50820390410180, ...
%e A182406   6, 630, 1166910, 38128724910, 21977869327169310, ...
%Y A182406 Columns k=1-7 give: A000027, A091940, A068239*2, A068240*2, A068241*2, A068242*2, A068243*2.
%Y A182406 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 A182406 Cf. A182368.
%K A182406 nonn,tabl
%O A182406 1,3
%A A182406 _Alois P. Heinz_, Apr 27 2012