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A296541
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.
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7
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1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 16, 8, 1, 1, 15, 37, 37, 15, 1, 1, 26, 96, 126, 96, 26, 1, 1, 45, 254, 431, 431, 254, 45, 1, 1, 80, 654, 1554, 2104, 1554, 654, 80, 1, 1, 140, 1709, 5601, 10734, 10734, 5601, 1709, 140, 1, 1, 245, 4472, 20036, 53995, 78660, 53995, 20036
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1....1.....1.......1........1.........1...........1............1
.1...3....5.....8......15.......26........45..........80..........140
.1...5...16....37......96......254.......654........1709.........4472
.1...8...37...126.....431.....1554......5601.......20036........71722
.1..15...96...431....2104....10734.....53995......270584......1360373
.1..26..254..1554...10734....78660....560942.....3987615.....28515358
.1..45..654..5601...53995...560942...5705431....57470370....581613058
.1..80.1709.20036..270584..3987615..57470370...820373528..11761387456
.1.140.4472.71722.1360373.28515358.581613058.11761387456.239372827502
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5)
k=3: [order 12]
k=4: [order 39]
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EXAMPLE
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Some solutions for n=6 k=4
..0..1..0..0. .0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..1..1..1
..0..1..1..0. .1..1..0..0. .0..0..0..0. .0..1..0..1. .0..1..1..0
..0..1..0..0. .1..0..0..1. .1..1..0..1. .0..1..1..0. .1..0..1..0
..1..1..1..0. .0..0..1..1. .1..0..1..1. .0..0..0..0. .1..0..1..0
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..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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