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A297374
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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