|
|
A241130
|
|
T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order
|
|
6
|
|
|
1, 2, 2, 4, 9, 4, 11, 54, 54, 11, 30, 325, 723, 325, 30, 82, 1965, 9773, 9773, 1965, 82, 224, 11876, 132369, 295584, 132369, 11876, 224, 612, 71793, 1792237, 8974020, 8974020, 1792237, 71793, 612, 1672, 434007, 24269723, 272418756, 611547441, 272418756
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Table starts
....1........2...........4..............11................30.................82
....2........9..........54.............325..............1965..............11876
....4.......54.........723............9773............132369............1792237
...11......325........9773..........295584...........8974020..........272418756
...30.....1965......132369.........8974020.........611547441........41661463219
...82....11876.....1792237.......272418756.......41661463219......6369134821236
..224....71793....24269723......8270609664.....2838552905280....973866422990563
..612...434007...328645291....251096788713...193403197619803.148910067386335603
.1672..2623694..4450319537...7623351508315.13177423185201303
.4568.15861001.60263615333.231446775293031
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
k=2: a(n) = 6*a(n-1) +2*a(n-2) -9*a(n-3) -10*a(n-4) +8*a(n-5) for n>6
k=3: [order 26]
|
|
EXAMPLE
|
Some solutions for n=3 k=4
..0..1..0..2....0..1..1..2....0..0..1..0....0..1..0..1....0..1..0..1
..1..0..2..2....0..2..2..0....1..1..2..0....0..2..1..2....2..2..1..2
..0..0..0..2....2..1..1..0....0..2..1..2....2..1..0..2....1..1..2..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|