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A317773
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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8
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1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 7, 5, 7, 8, 13, 11, 11, 11, 11, 13, 21, 18, 16, 10, 16, 18, 21, 34, 30, 28, 14, 14, 28, 30, 34, 55, 49, 44, 23, 19, 23, 44, 49, 55, 89, 81, 74, 32, 30, 30, 32, 74, 81, 89, 144, 134, 122, 55, 42, 40, 42, 55, 122, 134, 144, 233, 221, 209, 86, 67, 54, 54, 67
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OFFSET
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1,2
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COMMENTS
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Table starts
..1..2...3..5...8..13..21..34..55..89.144.233..377..610..987.1597.2584..4181
..2..3...4..7..11..18..30..49..81.134.221.365..603..996.1645.2717.4488..7413
..3..4...5.11..16..28..44..74.122.209.344.584..981.1670.2806.4758.8047.13665
..5..7..11.10..14..23..32..55..86.143.226.367..599..967.1581.2574.4220..6868
..8.11..16.14..19..30..42..67.100.160.248.401..630.1025.1615.2605.4136..6726
.13.18..28.23..30..40..54..82.115.185.266.425..649.1028.1588.2487.3908..6096
.21.30..44.32..42..54..75.107.149.221.317.491..739.1157.1774.2819.4306..6792
.34.49..74.55..67..82.107.159.209.296.408.604..862.1336.1951.3069.4613..7156
.55.81.122.86.100.115.149.209.310.405.554.784.1110.1634.2337.3542.5297..8100
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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)
k=2: a(n) = a(n-1) +2*a(n-3) -a(n-6)
k=3: [order 17] for n>23
k=4: [order 14] for n>23
k=5: [order 33] for n>41
k=6: [order 65] for n>72
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..1..1. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..1..1..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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