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A296386 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 2 neighboring 1s. 8
1, 2, 2, 4, 10, 4, 7, 28, 28, 7, 12, 86, 127, 86, 12, 21, 279, 641, 641, 279, 21, 37, 869, 3237, 5389, 3237, 869, 37, 65, 2728, 16248, 46786, 46786, 16248, 2728, 65, 114, 8596, 81661, 396806, 684894, 396806, 81661, 8596, 114, 200, 27004, 410199, 3372222 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4.........7..........12............21..............37
...2....10......28........86.........279...........869............2728
...4....28.....127.......641........3237.........16248...........81661
...7....86.....641......5389.......46786........396806.........3372222
..12...279....3237.....46786......684894.......9703136.......138882856
..21...869...16248....396806.....9703136.....229596763......5498685275
..37..2728...81661...3372222...138882856....5498685275....221204933878
..65..8596..410199..28724880..1988460073..131626644289...8887761158698
.114.27004.2061212.244493344.28434977556.3147315906687.356576134627608
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -5*a(n-6) +3*a(n-7) -a(n-8)
k=3: [order 16]
k=4: [order 40]
k=5: [order 92]
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..0. .1..0..0..1. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..0..0..1. .1..1..0..1. .1..0..0..1. .0..1..1..0
..0..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..0..0. .1..0..0..0
..0..1..0..1. .1..0..0..0. .0..1..1..0. .0..0..1..1. .1..0..0..0
..0..0..1..0. .1..1..0..0. .1..0..1..1. .0..0..0..0. .1..0..0..0
CROSSREFS
Column 1 is A005251(n+2).
Sequence in context: A308434 A121623 A267347 * A296643 A295040 A295531
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 11 2017
STATUS
approved

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Last modified April 23 03:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)