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A302265
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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13
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1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 153, 128, 16, 32, 384, 772, 818, 512, 32, 64, 1405, 3818, 5922, 4386, 2048, 64, 128, 5135, 19191, 40296, 45717, 23516, 8192, 128, 256, 18766, 96004, 284428, 429854, 353229, 126162, 32768, 256, 512, 68589, 481261
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2.......4.........8.........16...........32............64
...2......8......29.......105........384.........1405..........5135
...4.....32.....153.......772.......3818........19191.........96004
...8....128.....818......5922......40296.......284428.......1984001
..16....512....4386.....45717.....429854......4289139......41994750
..32...2048...23516....353229....4608075.....64975832.....893462062
..64...8192..126162...2727755...49315068....982041385...18964765818
.128..32768..676988..21069318..527911860..14850510984..402597400706
.256.131072.3632880.162753849.5651844495.224584502616.8547940665506
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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) = 6*a(n-1) -2*a(n-2) +2*a(n-3) -54*a(n-4) +16*a(n-5) for n>6
k=4: [order 17] for n>18
k=5: [order 70] for n>71
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 12] for n>13
n=4: [order 44] for n>45
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..1..0
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..0. .1..0..1..1
..1..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..1. .1..1..0..0
..0..1..1..1. .1..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..1
..1..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..1..0. .1..1..0..0
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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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