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

Author

R. H. Hardin, Jan 02 2013

Keywords

• nonn
• tabl

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.

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A090390.