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A208050
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).
9
1, 1, 1, 2, 2, 2, 5, 8, 8, 5, 14, 32, 44, 32, 14, 41, 128, 244, 244, 128, 41, 122, 512, 1356, 1904, 1356, 512, 122, 365, 2048, 7540, 14976, 14976, 7540, 2048, 365, 1094, 8192, 41932, 118096, 168096, 118096, 41932, 8192, 1094, 3281, 32768, 233204, 931968
OFFSET
1,4
COMMENTS
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
LINKS
EXAMPLE
Table starts
...1....1......2.......5........14.........41..........122...........365
...1....2......8......32.......128........512.........2048..........8192
...2....8.....44.....244......1356.......7540........41932........233204
...5...32....244....1904.....14976.....118096.......931968.......7356288
..14..128...1356...14976....168096....1897888.....21472544.....243113056
..41..512...7540..118096...1897888...30818432....502504448....8206614784
.122.2048..41932..931968..21472544..502504448..11838995200..279733684992
.365.8192.233204.7356288.243113056.8206614784.279733684992.9578237457408
...
Some solutions for n=4 k=3
..0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2
..2..3..1....2..3..0....2..3..1....2..3..1....2..0..3....2..3..0....2..0..3
..1..2..0....0..1..2....0..2..3....0..2..3....1..2..1....1..2..1....1..2..0
..3..1..2....2..3..1....1..0..1....3..0..2....3..0..3....3..0..2....3..1..2
CROSSREFS
Columns 1-7 are A007051(n-2), A004171(n-2), A208044, A208046, A208047-A208049.
Main diagonal is A208045.
Sequence in context: A365616 A162145 A374403 * A322176 A039886 A367087
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 22 2012
STATUS
approved