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

1,3

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A297870(n+2).

Sequence in context: A077901 A105619 A302212 * A303242 A302367 A303084

Adjacent sequences: A302457 A302458 A302459 * A302461 A302462 A302463

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 08 2018

Status

approved