A221139 T(n,k) = number of n X k arrays of occupancy after each element moves to some horizontal or vertical neighbor, with no occupancy greater than 2.

0, 1, 1, 2, 9, 2, 4, 49, 49, 4, 8, 289, 656, 289, 8, 16, 1681, 12544, 12544, 1681, 16, 32, 9801, 200072, 643204, 200072, 9801, 32, 64, 57121, 3485689, 31203396, 31203396, 3485689, 57121, 64, 128, 332929, 58132316, 1539699121, 4235650596, 1539699121

Offset

1,4

Comments

Table starts

....0........1............2...............4.................8

....1........9...........49.............289..............1681

....2.......49..........656...........12544............200072

....4......289........12544..........643204..........31203396

....8.....1681.......200072........31203396........4235650596

...16.....9801......3485689......1539699121......619901126244

...32....57121.....58132316.....75512292025....86907967843320

...64...332929....990486784...3709710975721.12474883501876324

..128..1940449..16699002692.182118668668225

..256.11309769.282999528529

..512.65918161

.1024

Even rows and columns are perfect squares.

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Example

Some solutions for n=3, k=4:
..1..1..1..2....1..1..1..1....1..1..0..2....1..1..2..1....1..1..2..0
..2..1..0..1....0..0..1..0....2..2..1..1....1..2..0..1....1..1..0..0
..0..1..2..0....2..2..2..1....0..0..2..0....0..2..0..1....1..2..1..2

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A090390.

Sequence in context: A153460 A342209 A248695 * A217273 A188981 A277754

Adjacent sequences: A221136 A221137 A221138 * A221140 A221141 A221142

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2013

Status

approved