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%I #9 Jun 26 2017 01:25:14
%S 1,1,1,2,2,2,5,8,8,5,14,32,44,32,14,41,128,244,244,128,41,122,512,
%T 1356,1904,1356,512,122,365,2048,7540,14976,14976,7540,2048,365,1094,
%U 8192,41932,118096,168096,118096,41932,8192,1094,3281,32768,233204,931968
%N T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
%C Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,k) using 4 colors up to permutation of the colors. - _Andrew Howroyd_, Jun 25 2017
%H R. H. Hardin, <a href="/A208050/b208050.txt">Table of n, a(n) for n = 1..312</a>
%e Table starts
%e ...1....1......2.......5........14.........41..........122...........365
%e ...1....2......8......32.......128........512.........2048..........8192
%e ...2....8.....44.....244......1356.......7540........41932........233204
%e ...5...32....244....1904.....14976.....118096.......931968.......7356288
%e ..14..128...1356...14976....168096....1897888.....21472544.....243113056
%e ..41..512...7540..118096...1897888...30818432....502504448....8206614784
%e .122.2048..41932..931968..21472544..502504448..11838995200..279733684992
%e .365.8192.233204.7356288.243113056.8206614784.279733684992.9578237457408
%e ...
%e Some solutions for n=4 k=3
%e ..0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2
%e ..2..3..1....2..3..0....2..3..1....2..3..1....2..0..3....2..3..0....2..0..3
%e ..1..2..0....0..1..2....0..2..3....0..2..3....1..2..1....1..2..1....1..2..0
%e ..3..1..2....2..3..1....1..0..1....3..0..2....3..0..3....3..0..2....3..1..2
%Y Columns 1-7 are A007051(n-2), A004171(n-2), A208044, A208046, A208047-A208049.
%Y Main diagonal is A208045.
%Y Cf. A208054, A068271, A212162, A212163.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Feb 22 2012
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