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A297506
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.
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13
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1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914
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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........7.........12...........21.............37
.1....10......31.......68........218..........729...........2097
.1....29.....110......314.......1829.........8803..........34757
.1....87.....531.....2281......23348.......191192........1247716
.1...280....2534....14201.....270845......3624914.......35049871
.1...876...11405....88808....3075264.....66289769......978288822
.1..2735...53175...573119...35919085...1272836591....28914051279
.1..8583..246040..3613793..414559944..23896899569...823340493402
.1.26900.1135117.22999331.4794512057.450529429259.23748019543354
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 11]
k=4: [order 18]
k=5: [order 50]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)
n=3: [order 10]
n=4: [order 24]
n=5: [order 59]
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..1..1. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..1. .0..1..0..0. .0..0..0..0
..1..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..1. .0..0..0..1
..1..1..0..0. .1..1..0..0. .1..1..0..0. .0..1..1..0. .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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