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A283691
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T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors.
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13
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2, 4, 4, 8, 16, 8, 16, 49, 57, 16, 32, 161, 264, 209, 32, 64, 548, 1521, 1525, 768, 64, 128, 1824, 8687, 15226, 8732, 2816, 128, 256, 6081, 47829, 149840, 150497, 49924, 10329, 256, 512, 20353, 268285, 1392868, 2530461, 1489917, 285770, 37889, 512, 1024
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OFFSET
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1,1
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COMMENTS
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Table starts
...2......4.......8.........16...........32.............64..............128
...4.....16......49........161..........548...........1824.............6081
...8.....57.....264.......1521.........8687..........47829...........268285
..16....209....1525......15226.......149840........1392868.........13354587
..32....768....8732.....150497......2530461.......39372084........640543058
..64...2816...49924....1489917.....42865601.....1119189256......30968693109
.128..10329..285770...14754038....726353972....31815868749....1496646288297
.256..37889.1635402..146079023..12304063774...904083654190...72299799564414
.512.138980.9359104.1446386879.208447516852.25694926726796.3493423029563345
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..264
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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) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).
k=3: [order 10].
k=4: [order 14].
k=5: [order 40].
k=6: [order 83].
Empirical for row n:
n=1: a(n) = 2*a(n-1).
n=2: a(n) = 3*a(n-1) +a(n-2) +3*a(n-3) -6*a(n-4) -8*a(n-5).
n=3: [order 11].
n=4: [order 23].
n=5: [order 56].
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EXAMPLE
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Some solutions for n=4, k=4
..1..0..1..1. .1..0..0..0. .0..0..1..0. .0..0..0..1. .1..0..1..0
..0..0..0..0. .1..0..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..0
..1..1..0..1. .0..1..0..0. .0..0..0..1. .0..1..1..0. .0..0..0..1
..1..0..0..1. .0..1..0..1. .1..0..0..1. .1..0..0..0. .0..0..0..1
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CROSSREFS
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Column 1 is A000079.
Column 2 is A283124.
Row 1 is A000079.
Sequence in context: A189343 A189779 A262338 * A283130 A295716 A282399
Adjacent sequences: A283688 A283689 A283690 * A283692 A283693 A283694
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 14 2017
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STATUS
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approved
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