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A268789
T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 13 2016
STATUS
approved