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A299052
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 11, 16, 8, 13, 50, 40, 40, 50, 13, 21, 112, 79, 455, 79, 112, 21, 34, 348, 480, 1650, 1650, 480, 348, 34, 55, 1028, 1542, 10706, 9994, 10706, 1542, 1028, 55, 89, 2796, 5317, 76068, 82340, 82340, 76068, 5317, 2796, 89, 144, 8216
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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
..2....4.....4......16.......50........112..........348...........1028
..3....4....11......40.......79........480.........1542...........5317
..5...16....40.....455.....1650......10706........76068.........445597
..8...50....79....1650.....9994......82340.......953445........8956381
.13..112...480...10706....82340....1731008.....29176924......456270494
.21..348..1542...76068...953445...29176924....888675946....23405238642
.34.1028..5317..445597..8956381..456270494..23405238642..1063108306477
.55.2796.22571.2902533.86708195.8295241404.693920505214.53324500523781
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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) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
k=3: [order 17] for n>18
k=4: [order 55] for n>58
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..0
..0..0..1..0. .0..0..0..1. .1..0..0..0. .1..0..0..0. .0..0..0..1
..0..0..1..1. .0..1..1..1. .1..1..0..0. .1..1..0..0. .1..1..0..0
..0..1..1..0. .0..0..0..1. .1..1..1..0. .1..1..0..1. .1..1..0..0
..0..1..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..1..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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