A297682 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

2, 4, 4, 7, 11, 8, 13, 29, 33, 16, 24, 80, 150, 98, 32, 44, 219, 629, 742, 291, 64, 81, 597, 2790, 4633, 3744, 865, 128, 149, 1632, 12110, 32911, 34872, 18840, 2570, 256, 274, 4459, 52889, 221420, 401678, 260924, 94891, 7637, 512, 504, 12181, 230406, 1519630

Offset: 1

Author

R. H. Hardin, Jan 03 2018

Keywords

• nonn
• tabl

Comments

Table starts

...2.....4.......7........13.........24...........44.............81

...4....11......29........80........219..........597...........1632

...8....33.....150.......629.......2790........12110..........52889

..16....98.....742......4633......32911.......221420........1519630

..32...291....3744.....34872.....401678......4202440.......45865837

..64...865...18840....260924....4870764.....78957968.....1368968852

.128..2570...94891...1955750...59210634...1487819051....41030621948

.256..7637..477850..14651847..719647644..28013761161..1229127412701

.512.22693.2406649.109783269.8748946600.527589764007.36837288191422

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Column 1 is A000079.

Column 2 is A282990.

Row 1 is A000073(n+3).

Row 2 is A124861(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -a(n-2) +8*a(n-3) -5*a(n-4) -30*a(n-5) +17*a(n-6)

k=4: [order 16]

k=5: [order 30]

k=6: [order 57]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2) +a(n-3)

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

n=3: [order 8]

n=4: [order 17]

n=5: [order 41]