A275352 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-2) and new values introduced in order 0..2.

1, 2, 2, 5, 14, 5, 14, 81, 54, 14, 41, 486, 288, 216, 41, 122, 2916, 1536, 1024, 864, 122, 365, 17496, 8192, 6156, 4100, 3456, 365, 1094, 104976, 43712, 38256, 31536, 16956, 13824, 1094, 3281, 629856, 235072, 239112, 266116, 175152, 70272, 55296, 3281

Offset: 1

Author

R. H. Hardin, Jul 24 2016

Keywords

• nonn
• tabl

Comments

Table starts

....1......2.......5........14..........41..........122............365

....2.....14......81.......486........2916........17496.........104976

....5.....54.....288......1536........8192........43712.........235072

...14....216....1024......6156.......38256.......239112........1530060

...41....864....4100.....31536......266116......2292520.......20917472

..122...3456...16956....175152.....2130176.....26615196......351504904

..365..13824...70272....982152....17258544....306863916.....5814135340

.1094..55296..291320...5645376...142784608...3682615020...101593710948

.3281.221184.1211092..33154200..1211010160..45094867336..1804283175916

.9842.884736.5070832.197081664.10285035212.548546009720.31575745629020

Examples

			Some solutions for n=4 k=4
..0..1..0..2. .0..1..1..2. .0..1..0..0. .0..1..1..1. .0..1..2..1
..1..0..1..0. .2..2..2..0. .1..2..2..0. .1..2..2..0. .0..2..1..2
..0..2..0..1. .0..2..0..0. .2..2..2..1. .2..2..0..0. .0..1..2..0
..2..2..1..0. .0..1..1..1. .0..0..1..1. .0..0..1..1. .0..2..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A208428.

Row 1 is A007051(n-1).

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2)

k=2: a(n) = 4*a(n-1) for n>3

k=3: [order 17] for n>20

Empirical for row n:

n=1: a(n) = 4*a(n-1) -3*a(n-2)

n=2: a(n) = 6*a(n-1) for n>3

n=3: [order 18] for n>20

n=4: [order 41] for n>43