A302460 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 44, 10, 177, 10, 64, 1, 123, 56, 233, 54, 474, 21, 128, 1, 266, 140, 123, 924, 111, 1397, 42, 256, 1, 499, 364, 1518, 1096, 3875, 276, 4135, 86, 512, 1, 1037, 764, 2945, 8869, 5266, 17189, 1050

Offset: 1

Author

R. H. Hardin, Apr 08 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1..1.....1....1......1......1........1.........1..........1...........1

...2..2....11...13.....34.....65......123.......266........499........1037

...4..2....18....8.....44.....56......140.......364........764........2352

...8..3....55...10....233....123.....1518......2945......16711.......58462

..16..6...177...54....924...1096.....8869.....29770.....176077......900973

..32.10...474..111...3875...5266....61254....287294....2165323....15547748

..64.21..1397..276..17189..25285...404761...2588958...25019102...250630168

.128.42..4135.1050..72529.149381..2822737..26036557..322917567..4472928245

.256.86.11882.3589.300519.866961.19107381.258817075.4110999261.79010238897

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..1..0..1. .0..1..1..0. .0..0..1..0
..0..0..1..1. .1..1..1..0. .0..1..0..1. .0..1..1..1. .0..0..1..0
..0..0..1..1. .1..1..1..1. .0..1..0..1. .1..1..0..1. .1..0..1..0
..1..1..0..0. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..0..1..0
..1..1..0..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A297870(n+2).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

k=3: [order 12]

k=4: [order 71] for n>72

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

n=3: [order 19] for n>20

n=4: [order 71] for n>72