A282647 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors.

2, 4, 4, 7, 11, 7, 13, 27, 27, 13, 24, 76, 99, 76, 24, 44, 201, 413, 413, 201, 44, 81, 537, 1601, 2638, 1601, 537, 81, 149, 1444, 6349, 15460, 15460, 6349, 1444, 149, 274, 3859, 25153, 92817, 133118, 92817, 25153, 3859, 274, 504, 10339, 99287, 557439, 1190848

Offset: 1

Author

R. H. Hardin, Feb 20 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

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

...7....27......99.......413.......1601.........6349..........25153

..13....76.....413......2638......15460........92817.........557439

..24...201....1601.....15460.....133118......1190848.......10614316

..44...537....6349.....92817....1190848.....15985259......213392087

..81..1444...25153....557439...10614316....213392087.....4257307148

.149..3859...99287...3332685...94161619...2835418176....84514081303

.274.10339..392907..19979228..838433062..37825158151..1685475197497

.504.27692.1553391.119669673.7454215075.503735487244.33544066527869

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..364

Crossrefs

Column 1 is A000073(n+3).

Formula

Empirical for column k:

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

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

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

k=4: [order 9]

k=5: [order 21]

k=6: [order 30]

k=7: [order 66]