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A302820
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 75, 81, 16, 32, 136, 220, 389, 264, 32, 64, 360, 731, 1494, 1852, 857, 64, 128, 960, 2419, 6905, 9050, 8485, 2785, 128, 256, 2576, 7900, 34957, 57684, 51476, 41247, 9050, 256, 512, 6944, 25645, 170262, 455224, 454733
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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............128
...2.....8.....20.......52.......136.........360..........960...........2576
...4....25.....75......220.......731........2419.........7900..........25645
...8....81....389.....1494......6905.......34957.......170262.........800847
..16...264...1852.....9050.....57684......455224......3252934.......21373833
..32...857...8485....51476....454733.....5520999.....58122740......535479917
..64..2785..41247...317216...3825201....72576189...1135257814....14619284475
.128..9050.196946..1927184..32123578...960564532..22294687742...402121386052
.256.29407.931243.11448173.264639685.12417289008.427140472935.10807066934912
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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) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 49] for n>51
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4
n=3: [order 15] for n>16
n=4: [order 67] for n>68
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..1..1..1. .1..1..1..1. .1..0..1..0. .1..0..0..0. .0..0..0..1
..0..1..0..1. .1..0..1..1. .1..1..1..1. .1..1..1..0. .1..0..1..1
..0..0..0..1. .1..1..0..1. .0..1..0..1. .1..0..1..0. .1..1..1..1
..1..1..1..0. .1..1..0..1. .0..1..0..0. .0..0..0..0. .0..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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