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A281205 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.

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