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 A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s. 13
 1, 2, 1, 4, 7, 1, 7, 23, 21, 1, 12, 66, 117, 65, 1, 21, 207, 497, 609, 200, 1, 37, 654, 2577, 3808, 3159, 616, 1, 65, 2049, 13937, 35476, 29212, 16389, 1897, 1, 114, 6422, 72541, 340825, 484808, 223995, 85041, 5842, 1, 200, 20119, 375054, 2997197, 8273245 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .1.....2.......4.........7..........12............21..............37 .1.....7......23........66.........207...........654............2049 .1....21.....117.......497........2577.........13937...........72541 .1....65.....609......3808.......35476........340825.........2997197 .1...200....3159.....29212......484808.......8273245.......121339476 .1...616...16389....223995.....6623719.....200646607......4893232934 .1..1897...85041...1717882....90535227....4869858862....197589351469 .1..5842..441225..13174266..1237278512..118156684121...7976248015498 .1.17991.2289339.101033369.16909630099.2867120332406.322003901582689 LINKS R. H. Hardin, Table of n, a(n) for n = 1..447 FORMULA Empirical for column k: k=1: a(n) = a(n-1) k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3) k=3: a(n) = 3*a(n-1) +11*a(n-2) +3*a(n-3) -6*a(n-4) k=4: [order 8] for n>9 k=5: [order 12] for n>14 k=6: [order 22] for n>25 k=7: [order 35] for n>39 Empirical for row n: n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) n=2: [order 9] n=3: [order 23] n=4: [order 61] EXAMPLE Some solutions for n=5 k=4 ..0..1..1..1. .1..1..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..0 ..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..1..1..1. .1..1..0..0 ..0..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1 ..1..1..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0 ..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..1..1. .1..0..1..1 CROSSREFS Column 2 is A218836. Row 1 is A005251(n+2). Sequence in context: A193591 A218842 A219421 * A220386 A219410 A221035 Adjacent sequences:  A297311 A297312 A297313 * A297315 A297316 A297317 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 28 2017 STATUS approved

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Last modified December 6 13:05 EST 2021. Contains 349563 sequences. (Running on oeis4.)