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A240636
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T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..1 introduced in row major order
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7
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1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 81, 129, 81, 16, 32, 264, 637, 637, 264, 32, 64, 857, 3147, 4989, 3147, 857, 64, 128, 2785, 15590, 38634, 38634, 15590, 2785, 128, 256, 9050, 77269, 299329, 470170, 299329, 77269, 9050, 256, 512, 29407, 382933, 2319211
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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
...2.....8......25.........81..........264............857.............2785
...4....25.....129........637.........3147..........15590............77269
...8....81.....637.......4989........38634.........299329..........2319211
..16...264....3147......38634.......470170........5723270.........69637692
..32...857...15590.....299329......5723270......109584463.......2097636322
..64..2785...77269....2319211.....69637692.....2097636322......63213422873
.128..9050..382933...17971509....847232955....40145256595....1904782876182
.256.29407.1897681..139264013..10307784448...768275538054...57392644533582
.512.95557.9404215.1079178635.125409399932.14702668840259.1729241310772922
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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) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 4*a(n-1) +4*a(n-2) +2*a(n-3) +7*a(n-4) +6*a(n-5) -a(n-6) -a(n-7) -a(n-8)
k=4: [order 32]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..0....0..0..1..0....0..1..1..1....0..0..1..0....0..0..0..1
..0..1..0..0....0..1..0..1....1..1..0..0....1..0..1..0....1..1..0..1
..1..0..1..1....1..0..0..1....1..0..0..0....1..0..0..1....0..0..1..0
..1..0..0..1....1..0..1..0....1..0..0..1....1..1..0..0....1..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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