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A306166
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 17, 9, 16, 32, 22, 32, 32, 22, 32, 64, 45, 77, 103, 77, 45, 64, 128, 101, 207, 298, 298, 207, 101, 128, 256, 218, 523, 962, 1188, 962, 523, 218, 256, 512, 477, 1304, 2966, 4849, 4849, 2966, 1304, 477, 512, 1024, 1041, 3307, 8756, 19176
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OFFSET
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1,2
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COMMENTS
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Table starts
...1...2....4.....8.....16......32.......64.......128........256.........512
...2...4....5.....9.....22......45......101.......218........477........1041
...4...5...17....32.....77.....207......523......1304.......3307........8414
...8...9...32...103....298.....962.....2966......8756......26287.......79873
..16..22...77...298...1188....4849....19176.....75681.....302442.....1206813
..32..45..207...962...4849...25226...128710....660871....3402775....17536734
..64.101..523..2966..19176..128710...842280...5553315...36528087...240890311
.128.218.1304..8756..75681..660871..5553315..47632142..405555135..3465256979
.256.477.3307.26287.302442.3402775.36528087.405555135.4469582265.49440451905
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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) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
k=3: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10
k=4: [order 18] for n>23
k=5: [order 40] for n>47
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
..1..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..0..0. .1..1..1..1
..0..0..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .1..0..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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