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A281205
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
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14
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0, 0, 0, 1, 2, 0, 2, 14, 10, 0, 5, 28, 56, 38, 0, 10, 52, 98, 168, 130, 0, 20, 94, 176, 270, 448, 420, 0, 38, 166, 310, 470, 676, 1120, 1308, 0, 71, 290, 537, 804, 1141, 1588, 2688, 3970, 0, 130, 502, 922, 1358, 1906, 2602, 3604, 6272, 11822, 0, 235, 864, 1573, 2284, 3137
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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....10.....20.....38.....71....130....235.....420
.0.....2....14....28....52....94....166....290....502....864...1480....2526
.0....10....56....98...176...310....537....922...1573...2672...4524....7640
.0....38...168...270...470...804...1358...2284...3834...6432..10786...18080
.0...130...448...676..1141..1906...3137...5160...8510..14084..23379...38894
.0...420..1120..1588..2602..4248...6838..11010..17840..29120..47838...78978
.0..1308..2688..3604..5712..9118..14375..22700..36144..58168..94524..154800
.0..3970..6272..7960.12208.19026..29416..45614..71452.113388.182228..295950
.0.11822.14336.17254.25577.38916..58984..89916.138676.217124.345089..555674
.0.34690.32256.36848.52784.78356.116466.174558.265278.409976.644568.1028978
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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) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
k=3: a(n) = 4*a(n-1) -4*a(n-2) for n>3
k=4: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -6*a(n-4) +2*a(n-5) +4*a(n-6) -a(n-8)
k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-4) +4*a(n-5) -a(n-8)
k=6: [order 12]
k=7: [order 12]
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
n=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>7
n=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>8
n=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>10
n=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>11
n=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>12
n=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>13
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1
..0..1..1..1. .0..1..0..0. .1..1..0..1. .1..0..1..0. .0..1..0..0
..0..1..0..0. .0..1..0..1. .0..1..0..1. .1..0..1..0. .1..0..1..1
..0..1..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..1. .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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