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A280554
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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7
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0, 0, 0, 0, 0, 0, 1, 9, 9, 1, 2, 34, 50, 34, 2, 6, 87, 144, 144, 87, 6, 13, 194, 325, 382, 325, 194, 13, 29, 400, 670, 832, 832, 670, 400, 29, 60, 790, 1316, 1666, 1764, 1666, 1316, 790, 60, 122, 1511, 2502, 3182, 3438, 3438, 3182, 2502, 1511, 122, 241, 2830, 4654
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OFFSET
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1,8
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COMMENTS
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Table starts
...0....0....0.....1.....2.....6....13.....29.....60....122....241....468
...0....0....9....34....87...194...400....790...1511...2830...5213...9484
...0....9...50...144...325...670..1316...2502...4654...8521..15412..27612
...1...34..144...382...832..1666..3182...5886..10680..19122..33920..59754
...2...87..325...832..1764..3438..6386..11506..20389..35757..62317.108150
...6..194..670..1666..3438..6502.11697..20440..35226..60300.102974.175746
..13..400.1316..3182..6386.11697.20334..34360..57389..95548.159360.266756
..29..790.2502..5886.11506.20440.34360..56102..90614.146264.237392.388378
..60.1511.4654.10680.20389.35226.57389..90614.141398.220709.347310.553046
.122.2830.8521.19122.35757.60300.95548.146264.220709.332810.506359.781682
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
k=2: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>9
k=3: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>10
k=4: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>11
k=5: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
k=6: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
k=7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..1. .1..0..1..1
..0..1..1..0. .1..0..1..0. .0..0..1..0. .1..0..1..0. .0..1..0..0
..1..0..1..0. .0..0..1..0. .1..1..0..1. .1..1..0..0. .0..1..0..1
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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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