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A302367
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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13
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1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 31, 3, 16, 1, 72, 20, 109, 6, 32, 1, 168, 154, 77, 397, 10, 64, 1, 496, 284, 918, 209, 1430, 21, 128, 1, 1296, 1109, 3125, 6580, 774, 5110, 42, 256, 1, 3616, 3472, 21831, 26458, 49293, 3143, 18395, 86, 512, 1, 9760, 12763, 125193
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OFFSET
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1,3
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COMMENTS
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Table starts
...1..1.....1.....1........1.........1...........1.............1
...2..2....12....20.......72.......168.........496..........1296
...4..2....31....20......154.......284........1109..........3472
...8..3...109....77......918......3125.......21831........125193
..16..6...397...209.....6580.....26458......405340.......3462040
..32.10..1430...774....49293....330505.....9361759.....134269527
..64.21..5110..3143...367512...3858625...188443738....4558781926
.128.42.18395.13556..2856621..48375470..4174802035..169314399506
.256.86.66203.60280.22185382.608124211.91302504318.6186362081201
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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) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 12]
k=4: [order 50] for n>53
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 16] for n>18
n=4: [order 63] for n>66
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..1..0. .0..0..1..1. .0..1..1..0
..1..1..1..1. .0..1..1..0. .0..0..1..0. .0..0..1..1. .1..1..1..1
..0..1..0..0. .1..1..1..1. .0..1..1..1. .0..1..1..0. .1..1..0..0
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0
..0..1..0..0. .0..0..0..1. .1..0..0..1. .0..0..1..1. .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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