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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. 14
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 LINKS R. H. Hardin, Table of n, a(n) for n = 1..421 FORMULA 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 EXAMPLE 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 CROSSREFS Row 1 is A001629(n-1). Sequence in context: A122496 A230813 A177113 * A285152 A077184 A077183 Adjacent sequences:  A281202 A281203 A281204 * A281206 A281207 A281208 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 17 2017 STATUS approved

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)