A221381 T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two

0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 4, 0, 1, 0, 0, 8, 9, 4, 0, 0, 0, 16, 0, 25, 0, 1, 0, 1, 32, 0, 189, 64, 8, 0, 0, 0, 64, 0, 1156, 0, 169, 0, 1, 0, 0, 128, 1225, 6996, 0, 5040, 441, 16, 0, 0, 0, 256, 0, 43681, 0, 120409, 0, 1156, 0, 1, 0, 1, 512, 0, 268632, 1397124, 2284160, 0, 134521

Offset

1,8

Comments

Table starts

.0.0..0.....1.......0..........0.........0...........1.........0...........0

.0.1..2.....4.......8.........16........32..........64.......128.........256

.0.0..0.....9.......0..........0.........0........1225.........0...........0

.0.1..4....25.....189.......1156......6996.......43681....268632.....1664100

.0.0..0....64.......0..........0.........0.....1397124.........0...........0

.0.1..8...169....5040.....120409...2284160....47527236.875241328.17328299769

.0.0..0...441.......0..........0.........0..1599280081.........0...........0

.0.1.16..1156..134521...13075456.763775056.54143705344

.0.0..0..3025.......0..........0.........0

.0.1.32..7921.3580920.1425817600

.0.0..0.20736.......0

.0.1.64.54289

Even columns are perfect squares

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Example

Some solutions for n=3 k=4
..0..2..2..0....0..2..2..0....0..2..2..2....0..2..0..2....0..2..2..0
..0..2..2..2....0..2..0..2....0..0..2..0....2..0..2..0....0..2..2..0
..0..0..2..0....2..0..2..0....0..2..2..0....0..2..2..0....0..2..2..0

Crossrefs

Column 4 is A007598(n+1)

Sequence in context: A204531 A113277 A114855 * A100951 A348616 A348613

Adjacent sequences: A221378 A221379 A221380 * A221382 A221383 A221384

Keyword

nonn,tabl

Author

R. H. Hardin Jan 14 2013

Status

approved