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A240039
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T(n,k)=Number of nXk 0..2 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 3
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7
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2, 2, 2, 4, 2, 4, 4, 6, 6, 4, 8, 4, 16, 4, 8, 8, 10, 16, 16, 10, 8, 16, 8, 42, 18, 42, 8, 16, 16, 20, 44, 52, 52, 44, 20, 16, 32, 16, 114, 62, 154, 62, 114, 16, 32, 32, 40, 122, 162, 178, 178, 162, 122, 40, 32, 64, 32, 314, 204, 494, 282, 494, 204, 314, 32, 64, 64, 80, 340, 530, 600
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OFFSET
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1,1
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COMMENTS
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Table starts
..2..2...4...4....8....8....16....16....32.....32.....64.....64.....128.....128
..2..2...6...4...10....8....20....16....40.....32.....80.....64.....160.....128
..4..6..16..16...42...44...114...122...314....340....872....950....2432....2658
..4..4..16..18...52...62...162...204...530....672...1736...2198....5706....7202
..8.10..42..52..154..178...494...600..1606...2014...5262...6690...17464...22360
..8..8..44..62..178..282...710..1074..2770...4162..10836..15764...41374...59680
.16.20.114.162..494..710..1976..2884..7958..12074..31824..49078..130758..197208
.16.16.122.204..600.1074..2884..5706.14686..25224..66774.113794..307698..508002
.32.40.314.530.1606.2770..7958.14686.42470..72446.200916.360716..984770.1730698
.32.32.340.672.2014.4162.12074.25224.72446.147092.407954.778294.2194512.4046228
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-2)
k=2: a(n) = 2*a(n-2) for n>5
k=3: a(n) = 4*a(n-2) -3*a(n-4) -a(n-6) for n>7
k=4: [order 24] for n>27
k=5: [order 86] for n>89
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EXAMPLE
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Some solutions for n=3 k=4
..2..1..1..2....2..1..2..1....2..1..2..1....1..2..1..2....1..2..1..2
..1..0..0..0....1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0
..1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0....2..0..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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