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A318082
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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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, 18, 22, 18, 18, 21, 34, 30, 32, 34, 34, 32, 30, 34, 55, 49, 54, 64, 51, 64, 54, 49, 55, 89, 81, 98, 132, 126, 126, 132, 98, 81, 89, 144, 134, 173, 280, 272, 314, 272, 280, 173, 134, 144, 233, 221, 315
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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
..2..3...4...7...11...18....30....49.....81....134.....221.....365......603
..3..4...5..11...18...32....54....98....173....315.....559....1008.....1813
..5..7..11..22...34...64...132...280....556...1083....2208....4480.....9083
..8.11..18..34...51..126...272...616...1347...2910....6602...15218....34152
.13.18..32..64..126..314...699..1778...4262..10254...25322...63395...158636
.21.30..54.132..272..699..1851..5189..13410..35181...97580..275205...756872
.34.49..98.280..616.1778..5189.15876..44305.131008..401009.1258378..3868741
.55.81.173.556.1347.4262.13410.44305.139346.466676.1583947.5508419.18965058
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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 24]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..1
..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..1..1..0. .0..0..0..0
..1..1..1..1. .0..1..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0
..0..1..1..1. .0..0..0..0. .0..1..1..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. .1..0..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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