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A297374
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s.
13
2, 4, 4, 8, 16, 8, 16, 57, 64, 16, 32, 208, 393, 256, 32, 64, 765, 2610, 2719, 1024, 64, 128, 2807, 17534, 33054, 18805, 4096, 128, 256, 10294, 116932, 409507, 418344, 130063, 16384, 256, 512, 37759, 780273, 4986469, 9554038, 5294713, 899565, 65536, 512
OFFSET
1,1
COMMENTS
Table starts
...2......4........8..........16............32..............64
...4.....16.......57.........208...........765............2807
...8.....64......393........2610.........17534..........116932
..16....256.....2719.......33054........409507.........4986469
..32...1024....18805......418344.......9554038.......211988289
..64...4096...130063.....5294713.....222925151......9012089653
.128..16384...899565....67012245....5201484239....383128155296
.256..65536..6221735...848136217..121365562862..16287817972455
.512.262144.43031893.10734382366.2831807366510.692439110062325
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -4*a(n-3)
k=4: a(n) = 13*a(n-1) -4*a(n-2) -3*a(n-3) -19*a(n-4) +15*a(n-5) -a(n-6)
k=5: [order 9] for n>11
k=6: [order 17] for n>19
k=7: [order 28] for n>31
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +5*a(n-3) +a(n-4) +a(n-5) -a(n-6) -a(n-7)
n=3: [order 12] for n>14
n=4: [order 29] for n>31
n=5: [order 84] for n>87
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0
..1..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0
..1..0..1..0. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..1..1..1
..1..0..0..0. .1..0..0..1. .0..1..0..0. .1..0..1..1. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..0..0. .1..0..0..1. .0..0..1..1
CROSSREFS
Column 1 is A000079.
Column 2 is A000302.
Row 1 is A000079.
Sequence in context: A283130 A295716 A282399 * A297102 A283415 A283857
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 29 2017
STATUS
approved