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A279384
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T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with new values introduced in order 0 sequentially upwards.
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8
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1, 1, 1, 1, 3, 1, 2, 8, 8, 2, 3, 22, 35, 22, 3, 5, 61, 157, 157, 61, 5, 8, 170, 695, 1101, 695, 170, 8, 13, 472, 3157, 7905, 7905, 3157, 472, 13, 21, 1310, 14243, 58009, 92803, 58009, 14243, 1310, 21, 34, 3637, 64170, 421999, 1098640, 1098640, 421999, 64170, 3637, 34
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OFFSET
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1,5
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COMMENTS
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Table starts
..1.....1.......1.........2...........3.............5...............8
..1.....3.......8........22..........61...........170.............472
..1.....8......35.......157.........695..........3157...........14243
..2....22.....157......1101........7905.........58009..........421999
..3....61.....695......7905.......92803.......1098640........12957948
..5...170....3157.....58009.....1098640......21144799.......404651396
..8...472...14243....421999....12957948.....404651396.....12564378389
.13..1310...64170...3067328...152622739....7733370493....389417147928
.21..3637..289200..22304530..1798168331..147824883279..12073180118618
.34.10099.1303737.162224094.21189754515.2826526873740.374420804035101
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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) +a(n-2) for n>3
k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) +3*a(n-4) +a(n-5)
k=3: [order 18]
k=4: [order 57] for n>58
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .0..0..1..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..0..0..0..1. .1..1..0..0. .1..0..0..0. .0..1..0..1. .1..0..1..0
..1..1..0..1. .0..1..1..0. .1..0..1..1. .0..1..0..0. .1..0..1..0
..0..0..1..0. .1..0..0..1. .1..0..0..1. .0..1..1..0. .1..0..0..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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