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A317383
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6, 7 or 8 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, 18, 9, 16, 32, 22, 36, 36, 22, 32, 64, 45, 94, 123, 94, 45, 64, 128, 101, 270, 414, 414, 270, 101, 128, 256, 218, 731, 1580, 2089, 1580, 731, 218, 256, 512, 477, 1973, 5704, 10732, 10732, 5704, 1973, 477, 512, 1024, 1041, 5388
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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
...2...4....5.....9......22.......45.......101........218..........477
...4...5...18....36......94......270.......731.......1973.........5388
...8...9...36...123.....414.....1580......5704......20162........72715
..16..22...94...414....2089....10732.....52617.....260141......1299431
..32..45..270..1580...10732....75405....508181....3446847.....23624322
..64.101..731..5704...52617...508181...4726521...44156330....416173164
.128.218.1973.20162..260141..3446847..44156330..569899203...7400913778
.256.477.5388.72715.1299431.23624322.416173164.7400913778.132364711390
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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) +3*a(n-2) +5*a(n-3) +2*a(n-4) -3*a(n-5) -10*a(n-6) -8*a(n-7) for n>10
k=4: [order 19] for n>23
k=5: [order 43] for n>49
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..1..0. .0..0..0..0. .1..0..1..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0
..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..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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