|
|
A208054
|
|
T(n,k) = Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
|
|
8
|
|
|
1, 1, 1, 2, 2, 2, 5, 15, 15, 5, 15, 203, 716, 203, 15, 52, 4140, 83440, 83440, 4140, 52, 203, 115975, 18171918, 112073062, 18171918, 115975, 203, 877, 4213597, 6423127757, 346212384169, 346212384169, 6423127757, 4213597, 877, 4140, 190899322
(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 any number of colors up to permutation of the colors. - Andrew Howroyd, Jun 25 2017
|
|
LINKS
|
|
|
EXAMPLE
|
Table starts
...1.........1.............2................5................15
...1.........2............15..............203..............4140
...2........15...........716............83440..........18171918
...5.......203.........83440........112073062......346212384169
..15......4140......18171918.....346212384169.18633407199331522
..52....115975....6423127757.2043836452962923
.203...4213597.3376465219485
.877.190899322
...
Some solutions for n=4 k=3
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
..2..3..1....2..3..4....2..3..2....2..3..1....2..3..0....2..3..1....2..3..2
..4..2..4....0..5..0....0..4..0....0..4..5....4..5..3....4..5..3....0..1..4
..0..5..0....1..2..1....1..2..1....5..3..4....0..1..0....0..6..4....2..0..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|