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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A001629.

Sequence in context: A166376 A089122 A321577 * A269920 A240706 A240642

Adjacent sequences: A268786 A268787 A268788 * A268790 A268791 A268792

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved