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

1,4

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: A365616 A162145 A374403 * A322176 A039886 A367087

Adjacent sequences: A208047 A208048 A208049 * A208051 A208052 A208053

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 22 2012

Status

approved