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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000073(n+3).

Sequence in context: A238493 A362937 A268781 * A269089 A282862 A296578

Adjacent sequences: A282644 A282645 A282646 * A282648 A282649 A282650

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2017

Status

approved