A268789 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

0, 1, 1, 2, 5, 2, 5, 17, 17, 5, 10, 48, 72, 48, 10, 20, 131, 302, 302, 131, 20, 38, 338, 1144, 1714, 1144, 338, 38, 71, 850, 4207, 9085, 9085, 4207, 850, 71, 130, 2091, 14984, 46195, 67100, 46195, 14984, 2091, 130, 235, 5061, 52335, 228384, 477128, 477128, 228384

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0.....1......2........5........10..........20............38.............71

...1.....5.....17.......48.......131.........338...........850...........2091

...2....17.....72......302......1144........4207.........14984..........52335

...5....48....302.....1714......9085.......46195........228384........1105510

..10...131...1144.....9085.....67100......477128.......3295246.......22302699

..20...338...4207....46195....477128.....4725018......45515227......429442918

..38...850..14984...228384...3295246....45515227.....611932378.....8057509992

..71..2091..52335..1105510..22302699...429442918....8057509992...148013550916

.130..5061.179854..5267662.148575958..3988796543..104456486696..2677312316674

.235.12095.610504.24786180.977609634.36591758790.1337467436839.47829470133134

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1404

Crossrefs

Column 1 is A001629.

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 16]

k=5: [order 26]

k=6: [order 42]

k=7: [order 68]