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A283042
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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.
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8
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0, 0, 0, 1, 4, 1, 2, 16, 16, 2, 5, 68, 119, 68, 5, 12, 256, 818, 818, 256, 12, 26, 924, 5065, 9152, 5065, 924, 26, 56, 3232, 30378, 94368, 94368, 30378, 3232, 56, 118, 11044, 175963, 931844, 1604067, 931844, 175963, 11044, 118, 244, 37104, 997302, 8912378
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OFFSET
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1,5
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COMMENTS
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Table starts
...0......0........1..........2.............5..............12................26
...0......4.......16.........68...........256.............924..............3232
...1.....16......119........818..........5065...........30378............175963
...2.....68......818.......9152.........94368..........931844...........8912378
...5....256.....5065......94368.......1604067........26180826.........414085368
..12....924....30378.....931844......26180826.......706205768.......18455711930
..26...3232...175963....8912378.....414085368.....18455711930......797350288363
..56..11044...997302...83420984....6406597648....471954803540....33705434438284
.118..37104..5559013..767704036...97480211225..11868995624930..1401215705047092
.244.122984.30578068.6973000128.1463896864692.294610925837548.57496998569457406
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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) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)
k=3: [order 18]
k=4: [order 30]
k=5: [order 72]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0. .1..0..0..0. .1..0..1..0. .0..0..1..1. .1..0..0..1
..1..0..1..0. .1..1..0..0. .0..1..1..1. .0..1..0..0. .0..1..0..1
..0..0..1..0. .0..0..1..0. .1..0..1..0. .1..0..1..0. .0..1..0..1
..1..0..0..0. .1..0..1..0. .1..0..0..0. .1..1..0..0. .0..0..0..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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