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%I #4 Jan 17 2017 08:21:56
%S 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,
%T 448,420,0,38,166,310,470,676,1120,1308,0,71,290,537,804,1141,1588,
%U 2688,3970,0,130,502,922,1358,1906,2602,3604,6272,11822,0,235,864,1573,2284,3137
%N 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.
%C Table starts
%C .0.....0.....1.....2.....5....10.....20.....38.....71....130....235.....420
%C .0.....2....14....28....52....94....166....290....502....864...1480....2526
%C .0....10....56....98...176...310....537....922...1573...2672...4524....7640
%C .0....38...168...270...470...804...1358...2284...3834...6432..10786...18080
%C .0...130...448...676..1141..1906...3137...5160...8510..14084..23379...38894
%C .0...420..1120..1588..2602..4248...6838..11010..17840..29120..47838...78978
%C .0..1308..2688..3604..5712..9118..14375..22700..36144..58168..94524..154800
%C .0..3970..6272..7960.12208.19026..29416..45614..71452.113388.182228..295950
%C .0.11822.14336.17254.25577.38916..58984..89916.138676.217124.345089..555674
%C .0.34690.32256.36848.52784.78356.116466.174558.265278.409976.644568.1028978
%H R. H. Hardin, <a href="/A281205/b281205.txt">Table of n, a(n) for n = 1..421</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
%F k=3: a(n) = 4*a(n-1) -4*a(n-2) for n>3
%F 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)
%F k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-4) +4*a(n-5) -a(n-8)
%F k=6: [order 12]
%F k=7: [order 12]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F n=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>7
%F n=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>8
%F 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
%F 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
%F 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
%F 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
%e Some solutions for n=4 k=4
%e ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1
%e ..0..1..1..1. .0..1..0..0. .1..1..0..1. .1..0..1..0. .0..1..0..0
%e ..0..1..0..0. .0..1..0..1. .0..1..0..1. .1..0..1..0. .1..0..1..1
%e ..0..1..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..1. .1..0..0..1
%Y Row 1 is A001629(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 17 2017
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