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A281715
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T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
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13
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1, 1, 2, 1, 3, 4, 2, 7, 4, 8, 3, 14, 8, 6, 16, 5, 29, 38, 14, 9, 32, 8, 61, 90, 97, 17, 14, 64, 13, 126, 305, 294, 245, 22, 22, 128, 21, 265, 902, 1410, 937, 631, 30, 35, 256, 34, 553, 2710, 5781, 6417, 3166, 1625, 43, 56, 512, 55, 1162, 8376, 23798, 37781, 29849, 10738, 4234
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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.....2......3........5.........8..........13...........21
...2..3..7....14.....29.......61.......126.........265..........553
...4..4..8....38.....90......305.......902........2710.........8376
...8..6.14....97....294.....1410......5781.......23798.......103034
..16..9.17...245....937.....6417.....37781......214045......1321909
..32.14.22...631...3166....29849....252867.....1987696.....17241122
..64.22.30..1625..10738...142023...1721319....18779855....230037168
.128.35.43..4234..37285...677045..11737418...178547832...3076165855
.256.56.64.11017.129586..3244671..80326035..1704685390..41247350230
.512.90.98.28652.452042.15605137.550174620.16297041786.554236736742
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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-3) for n>4
k=3: a(n) = 2*a(n-1) -a(n-3) for n>6
k=4: [order 15] for n>16
k=5: [order 24] for n>28
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5)
n=3: [order 20] for n>21
n=4: [order 72] for n>73
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..0..1..1. .0..0..0..1
..1..1..0..1. .1..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..1..1
..1..1..1..0. .1..1..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..1
..1..1..0..0. .0..0..0..0. .0..0..1..0. .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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