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 A297395 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1. 12
 1, 2, 1, 3, 5, 1, 4, 9, 9, 1, 6, 13, 19, 20, 1, 9, 33, 37, 57, 41, 1, 13, 69, 127, 126, 139, 85, 1, 19, 121, 323, 700, 385, 369, 178, 1, 28, 253, 763, 2569, 3175, 1243, 963, 369, 1, 41, 529, 2121, 7779, 14940, 15541, 3924, 2489, 769, 1, 60, 1013, 5557, 31081, 58901, 99682 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .1...2....3.....4.......6........9........13.........19...........28 .1...5....9....13......33.......69.......121........253..........529 .1...9...19....37.....127......323.......763.......2121.........5557 .1..20...57...126.....700.....2569......7779......31081.......117084 .1..41..139...385....3175....14940.....58901.....325922......1616869 .1..85..369..1243...15541....99682....514945....3977868.....27131403 .1.178..963..3924...74736...640562...4279111...46261441....428200086 .1.369.2489.12477..358341..4101278..35870939..540319235...6780786267 .1.769.6523.39625.1729617.26607999.302197213.6362528482.108762242579 LINKS R. H. Hardin, Table of n, a(n) for n = 1..420 FORMULA Empirical for column k: k=1: a(n) = a(n-1) k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4) k=3: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -4*a(n-4) k=4: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -3*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) k=5: [order 20] k=6: [order 25] k=7: [order 55] Empirical for row n: n=1: a(n) = a(n-1) +a(n-3) n=2: a(n) = a(n-1) +4*a(n-3) n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +a(n-4) -2*a(n-6) n=4: [order 8] n=5: [order 21] n=6: [order 31] n=7: [order 69] EXAMPLE Some solutions for n=5 k=4 ..0..0..1..1. .0..1..1..0. .0..1..0..0. .0..0..1..1. .0..0..0..0 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0 ..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..1 ..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..0..0 ..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..0..0. .1..0..0..0 CROSSREFS Column 2 is A105309(n+1). Row 1 is A000930(n+1). Row 2 is A089977(n+1). Sequence in context: A047997 A188211 A175009 * A297595 A049069 A030237 Adjacent sequences: A297392 A297393 A297394 * A297396 A297397 A297398 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 29 2017 STATUS approved

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Last modified August 8 18:48 EDT 2024. Contains 375023 sequences. (Running on oeis4.)