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A303197
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 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, 12, 10, 16, 13, 25, 23, 23, 21, 32, 21, 65, 43, 46, 62, 42, 64, 34, 185, 105, 97, 185, 122, 86, 128, 55, 385, 233, 283, 523, 497, 305, 179, 256, 89, 649, 479, 687, 2106, 1751, 1357, 793, 370, 512, 144, 1489, 968, 1642, 7425, 8250, 5573
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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
...2...3....9....17....25.....65.....185......385.......649.......1489
...4...6...12....23....43....105.....233......479.......968.......2146
...8..10...23....46....97....283.....687.....1642......3949......10169
..16..21...62...185...523...2106....7425....23976.....77199.....278516
..32..42..122...497..1751...8250...34801...138014....547379....2363422
..64..86..305..1357..5573..32223..164295...791150...3806973...20061588
.128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170
.256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370
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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: [order 7] for n>11
k=4: [order 42] for n>43
k=5: [order 33] for n>37
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: [order 18] for n>19
n=4: [order 70] for n>71
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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..1..0..1. .0..1..1..0
..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..1
..1..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1. .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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