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A300350
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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8
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0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 9, 15, 3, 5, 37, 26, 26, 37, 5, 8, 90, 57, 58, 57, 90, 8, 13, 223, 133, 152, 152, 133, 223, 13, 21, 550, 306, 325, 306, 325, 306, 550, 21, 34, 1355, 709, 729, 729, 729, 729, 709, 1355, 34, 55, 3341, 1642, 1609, 1496, 1371, 1496, 1609
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OFFSET
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1,5
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COMMENTS
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Table starts
..0....1....1....2....3.....5.....8....13....21.....34.....55.....89.....144
..1....2....6...15...37....90...223...550..1355...3341...8237..20307...50064
..1....6....9...26...57...133...306...709..1642...3805...8811..20409...47276
..2...15...26...58..152...325...729..1609..3577...7931..17605..39106...86859
..3...37...57..152..306...729..1496..3223..6893..14847..31957..68842..148439
..5...90..133..325..729..1371..3092..6068.12638..26306..55227.116124..244628
..8..223..306..729.1496..3092..5451.12038.22852..46541..95132.196177..405629
.13..550..709.1609.3223..6068.12038.20316.44961..83436.167732.339040..690762
.21.1355.1642.3577.6893.12638.22852.44961.73826.165976.303634.606479.1218187
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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-2) +3*a(n-3) +2*a(n-4) +a(n-5)
k=3: a(n) = 2*a(n-1) +a(n-2) -2*a(n-5) -2*a(n-6) -2*a(n-7) -a(n-8) for n>10
k=4: [order 13] for n>16
k=5: [order 15] for n>19
k=6: [order 17] for n>22
k=7: [order 19] for n>25
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..1. .0..1..1..1
..1..0..0..1. .0..1..1..1. .1..1..1..0. .0..1..0..0. .0..0..0..1
..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..0..1..0. .1..1..0..0
..0..1..1..1. .1..1..1..0. .1..0..0..1. .1..1..0..1. .0..1..1..0
..0..0..0..0. .0..0..1..0. .1..1..0..0. .0..0..1..1. .0..0..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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