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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 (list; table; graph; refs; listen; history; text; internal format)
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

R. H. Hardin, Table of n, a(n) for n = 1..312

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.

Cf. A208054, A068271, A212162, A212163.

Sequence in context: A240540 A039878 A162145 * A322176 A039886 A109523

Adjacent sequences:  A208047 A208048 A208049 * A208051 A208052 A208053

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 22 2012

STATUS

approved

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Last modified July 4 14:51 EDT 2020. Contains 335448 sequences. (Running on oeis4.)