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A302427
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 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, 11, 10, 16, 13, 25, 21, 21, 21, 32, 21, 65, 38, 42, 51, 42, 64, 34, 185, 88, 83, 148, 93, 86, 128, 55, 385, 188, 235, 372, 362, 207, 179, 256, 89, 649, 377, 532, 1359, 992, 879, 517, 370, 512, 144, 1489, 735, 1250, 4223, 4231, 2503, 2447
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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...11...21....38.....88....188.....377......735......1557.......3288
...8..10...21...42....83....235....532....1250.....2839......6972......16274
..16..21...51..148...372...1359...4223...12765....36991....120577.....379049
..32..42...93..362...992...4231..14764...53851...182216....685166....2496115
..64..86..207..879..2503..12527..48037..204549...775916...3358602...13687791
.128.179..517.2447..7611..49454.227283.1171867..5110314..27366139..134037982
.256.370.1007.6306.21321.179252.940829.6104653.30957683.207165078.1213329113
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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) +10*a(n-3) -8*a(n-4) for n>9
k=4: [order 42] for n>43
k=5: [order 21] for n>24
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 68] for n>69
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..1..0..1. .0..1..0..0. .1..1..0..1
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..0
..1..0..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..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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