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

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

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

R. H. Hardin, Table of n, a(n) for n = 1..97

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

Column 1 is A021006(n-3)

Sequence in context: A280859 A280961 A280362 * A019822 A322765 A281605

Adjacent sequences: A241127 A241128 A241129 * A241131 A241132 A241133

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 16 2014

Status

approved