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A301662
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically 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, 6, 6, 6, 8, 13, 9, 9, 9, 9, 13, 21, 14, 15, 13, 15, 14, 21, 34, 22, 26, 24, 24, 26, 22, 34, 55, 35, 46, 45, 46, 45, 46, 35, 55, 89, 56, 83, 89, 99, 99, 89, 83, 56, 89, 144, 90, 151, 182, 223, 254, 223, 182, 151, 90, 144, 233, 145, 276, 373, 528, 696
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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
..2..3...4...6....9...14....22.....35......56......90......145.......234
..3..4...6...9...15...26....46.....83.....151.....276......506.......929
..5..6...9..13...24...45....89....182.....373.....773.....1604......3333
..8..9..15..24...46...99...223....528....1268....3085.....7557.....18564
.13.14..26..45...99..254...696...2013....5953...17878....54126....164525
.21.22..46..89..223..696..2335...8380...31001..116558...442314...1686894
.34.35..83.182..528.2013..8380..37679..175638..833737..4001569..19319239
.55.56.151.373.1268.5953.31001.175638.1036686.6245327.38085186.233683529
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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) = 2*a(n-1) -a(n-3)
k=3: a(n) = 2*a(n-1) -a(n-4)
k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=5: [order 11]
k=6: [order 18]
k=7: [order 31]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..1..0..1. .1..0..1..0. .1..1..1..0. .1..0..1..0. .1..0..1..0
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..1
..1..1..0..1. .1..1..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..0
..0..0..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..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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