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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000079.

Column 2 is A282990.

Row 1 is A000073(n+3).

Row 2 is A282641.

Sequence in context: A295253 A295652 A269075 * A297682 A297607 A223770

Adjacent sequences: A283540 A283541 A283542 * A283544 A283545 A283546

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 10 2017

Status

approved