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A299886
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 7 or 8 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, 10, 16, 8, 13, 50, 28, 28, 50, 13, 21, 112, 44, 247, 44, 112, 21, 34, 348, 222, 677, 677, 222, 348, 34, 55, 1028, 573, 3597, 3127, 3597, 573, 1028, 55, 89, 2796, 1551, 21500, 16277, 16277, 21500, 1551, 2796, 89, 144, 8216, 5437, 101350
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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
..2....4....4.....16......50.......112.........348.........1028...........2796
..3....4...10.....28......44.......222.........573.........1551...........5437
..5...16...28....247.....677......3597.......21500.......101350.........547390
..8...50...44....677....3127.....16277......154308......1009789........7044041
.13..112..222...3597...16277....223094.....2596017.....24865898......323299576
.21..348..573..21500..154308...2596017....56762816....870847276....16820882455
.34.1028.1551.101350.1009789..24865898...870847276..20496493815...621532095596
.55.2796.5437.547390.7044041.323299576.16820882455.621532095596.32439092859262
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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 18] for n>19
k=4: [order 66] for n>68
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..1. .0..1..1..1. .0..1..1..0. .0..0..0..0
..1..1..0..0. .0..0..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..1
..1..1..0..1. .0..0..1..1. .1..0..0..0. .1..1..1..1. .1..1..1..1
..1..0..0..0. .1..1..1..1. .1..1..0..1. .0..0..0..0. .0..0..1..0
..1..0..0..1. .0..0..1..0. .1..1..0..1. .1..1..0..0. .0..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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