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).

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

Author

R. H. Hardin, Feb 22 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Columns 1-7 are A007051(n-2), A004171(n-2), A208044, A208046, A208047-A208049.

Main diagonal is A208045.

Cf. A208054, A068271, A212162, A212163.