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 A281056 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 two elements, and with new values introduced in order 0 sequentially upwards. 14
 0, 0, 0, 0, 1, 0, 1, 6, 6, 0, 2, 34, 68, 29, 0, 6, 104, 239, 376, 122, 0, 13, 251, 618, 1022, 1492, 468, 0, 29, 535, 1403, 2452, 3416, 4988, 1686, 0, 60, 1076, 2828, 5400, 7803, 10112, 15028, 5807, 0, 122, 2090, 5482, 10570, 16875, 22106, 27635, 42252, 19338, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Table starts .0.....0......0......1......2.......6......13......29......60......122......241 .0.....1......6.....34....104.....251.....535....1076....2090.....3956.....7353 .0.....6.....68....239....618....1403....2828....5482...10342....19136....34907 .0....29....376...1022...2452....5400...10570...19892...36616....66354...118926 .0...122...1492...3416...7803...16875...32370...59669..107693...191953...339219 .0...468...4988..10112..22106...46610...87995..159317..282552...495655...864369 .0..1686..15028..27635..58005..119205..221212..394884..689397..1191475..2050466 .0..5807..42252..71419.144283..288527..526340..926077.1596265..2721514..4625355 .0.19338.113076.177320.344972..671451.1201939.2084979.3549039..5982952.10051523 .0.62731.291660.426696.800225.1515524.2661939.4546633.7645715.12749511.21211441 LINKS R. H. Hardin, Table of n, a(n) for n = 1..338 FORMULA Empirical for column k: k=1: a(n) = a(n-1) k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6) k=3: a(n) = 5*a(n-1) -6*a(n-2) -4*a(n-3) +8*a(n-4) for n>6 k=4: [order 12] for n>14 k=5: [order 13] for n>16 k=6: [order 18] for n>21 k=7: [order 19] for n>23 Empirical for row n: n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6) n=2: [order 8] for n>14 n=3: [same order 8] for n>15 n=4: [order 9] for n>17 n=5: [same order 9] for n>18 n=6: [same order 9] for n>19 n=7: [same order 9] for n>20 EXAMPLE Some solutions for n=4 k=4 ..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1 ..1..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .1..0..1..1 ..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..0..1. .1..0..0..1 ..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..0..1..1. .1..0..1..0 CROSSREFS Row 1 is A055243(n-4). Sequence in context: A283203 A155742 A005597 * A273989 A197013 A329092 Adjacent sequences:  A281053 A281054 A281055 * A281057 A281058 A281059 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 13 2017 STATUS approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)