A283543 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.

2, 4, 4, 7, 11, 8, 13, 27, 33, 16, 24, 76, 127, 98, 32, 44, 201, 578, 573, 291, 64, 81, 537, 2369, 4089, 2615, 865, 128, 149, 1444, 10069, 25532, 29558, 11903, 2570, 256, 274, 3859, 42664, 167920, 282773, 212441, 54211, 7637, 512, 504, 10339, 179733, 1094959

Offset: 1

Author

R. H. Hardin, Mar 10 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

....4....11......27........76.........201...........537............1444

....8....33.....127.......578........2369.........10069...........42664

...16....98.....573......4089.......25532........167920.........1094959

...32...291....2615.....29558......282773.......2905717........29377334

...64...865...11903....212441.....3109801......49760703.......778500603

..128..2570...54211...1529463....34266804.....854841910.....20707472573

..256..7637..246869..11006233...377393657...14672363665....550220030803

..512.22693.1124239..79212552..4156954825..251901309671..14624495679716

.1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..313

Crossrefs

Column 1 is A000079.

Column 2 is A282990.

Row 1 is A000073(n+3).

Row 2 is A282641.

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) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)

k=4: [order 8]

k=5: [order 21]

k=6: [order 27]

k=7: [order 59]

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)

n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)

n=4: [order 8]

n=5: [order 21]

n=6: [order 32]

n=7: [order 69]