A297637 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.

2, 3, 4, 5, 8, 8, 8, 29, 20, 16, 13, 69, 113, 51, 32, 21, 200, 374, 494, 132, 64, 34, 552, 1657, 2370, 2344, 341, 128, 55, 1641, 6548, 17305, 16508, 10587, 883, 256, 89, 4685, 28645, 108928, 201152, 109790, 48187, 2293, 512, 144, 13716, 119531, 771393

Offset

1,1

Comments

Table starts

...2....3.......5........8.........13...........21.............34

...4....8......29.......69........200..........552...........1641

...8...20.....113......374.......1657.........6548..........28645

..16...51.....494.....2370......17305.......108928.........771393

..32..132....2344....16508.....201152......2077060.......25139952

..64..341...10587...109790....2171757.....36084211......715726580

.128..883...48187...740555...24145671....659362756....21730243952

.256.2293..222804..5099557..273842684..12330890209...681285029028

.512.5964.1027173.35164860.3092881435.229556423760.21128576143262

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) = 4*a(n-1) -3*a(n-2) -4*a(n-4) -a(n-5) +a(n-6)

k=3: [order 15]

k=4: [order 32]

k=5: [order 68]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

n=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) +6*a(n-4) -28*a(n-5) -24*a(n-6)

n=3: [order 18]

n=4: [order 40]

Example

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

Crossrefs

Column 1 is A000079.

Column 2 is A295346.

Row 1 is A000045(n+2).

Sequence in context: A297338 A297457 A297694 * A325415 A331076 A316496

Adjacent sequences: A297634 A297635 A297636 * A297638 A297639 A297640

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2018

Status

approved