A295652 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1, 3 or 4 1s.

2, 4, 4, 7, 11, 7, 13, 35, 35, 13, 24, 106, 184, 106, 24, 44, 327, 956, 956, 327, 44, 81, 1003, 4993, 8391, 4993, 1003, 81, 149, 3082, 26037, 74335, 74335, 26037, 3082, 149, 274, 9465, 135848, 657178, 1117226, 657178, 135848, 9465, 274, 504, 29073, 708695

Offset

1,1

Comments

Table starts

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

...4....11......35.......106.........327..........1003............3082

...7....35.....184.......956........4993.........26037..........135848

..13...106.....956......8391.......74335........657178.........5812860

..24...327....4993.....74335.....1117226......16755140.......251412699

..44..1003...26037....657178....16755140.....426233396.....10849299317

..81..3082..135848...5812860...251412699...10849299317....468469936974

.149..9465..708695..51408810..3772052117..276124405949..20225972157848

.274.29073.3697224.454678898.56595784982.7027872154812.873281057421907

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3) -a(n-5)

k=3: [order 18]

k=4: [order 45]

Example

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

Crossrefs

Column 1 is A000073(n+3).

Column 2 is A295247.

Sequence in context: A282996 A295275 A295253 * A269075 A283543 A297682

Adjacent sequences: A295649 A295650 A295651 * A295653 A295654 A295655

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 25 2017

Status

approved