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A302635
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 8, 10, 16, 13, 25, 14, 19, 21, 32, 21, 65, 25, 33, 42, 42, 64, 34, 185, 47, 65, 101, 82, 86, 128, 55, 385, 83, 149, 257, 248, 189, 179, 256, 89, 649, 150, 304, 691, 719, 657, 469, 370, 512, 144, 1489, 269, 643, 1734, 2262, 2303, 1841, 1029
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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
...2...3....9...17....25.....65....185.....385......649.....1489......3929
...4...6....8...14....25.....47.....83.....150......269......488.......876
...8..10...19...33....65....149....304.....643.....1343.....2880......6038
..16..21...42..101...257....691...1734....4502....11524....30121.....77399
..32..42...82..248...719...2262...6460...19799....59002...179668....535412
..64..86..189..657..2303...8981..30216..112431...408512..1512824...5441957
.128.179..469.1841..7695..35772.144266..652931..2863575.12800635..55765517
.256.370.1029.4892.24205.135125.642553.3499587.18446157.98898783.515558643
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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-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = a(n-1) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13
k=4: [order 21] for n>25
k=5: [order 29] for n>32
k=6: [order 54] for n>65
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: a(n) = a(n-1) +a(n-2) +2*a(n-4) -a(n-5) for n>7
n=4: [order 22] for n>23
n=5: [order 63] for n>64
n=6: [order 81] for n>86
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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..0..1..1. .0..1..0..1
..1..1..1..0. .0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .0..1..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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