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 A297224 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s. 12
 1, 2, 1, 3, 4, 1, 4, 8, 9, 1, 6, 16, 24, 19, 1, 9, 33, 57, 68, 41, 1, 13, 69, 182, 207, 196, 88, 1, 19, 145, 535, 997, 751, 564, 189, 1, 28, 300, 1513, 4210, 5570, 2720, 1620, 406, 1, 41, 624, 4415, 16658, 33158, 30946, 9861, 4660, 872, 1, 60, 1300, 12832, 68769, 178469 (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...4.....8.....16......33........69........145.........300...........624 .1...9....24.....57.....182.......535.......1513........4415.........12832 .1..19....68....207.....997......4210......16658.......68769........284867 .1..41...196....751....5570.....33158.....178469.....1051514.......6152761 .1..88...564...2720...30946....261939....1918732....16176806.....134671502 .1.189..1620...9861..171851...2063378...20599895...248421807....2936448567 .1.406..4660..35741..955316..16277793..221333623..3819208252...64142817874 .1.872.13396.129540.5308160.128351805.2377449633.58680928294.1400212345305 LINKS R. H. Hardin, Table of n, a(n) for n = 1..611 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) k=3: a(n) = a(n-1) +4*a(n-2) +4*a(n-3) k=4: a(n) = a(n-1) +6*a(n-2) +11*a(n-3) +6*a(n-4) +a(n-5) k=5: [order 9] k=6: [order 11] for n>13 k=7: [order 16] for n>21 Empirical for row n: n=1: a(n) = a(n-1) +a(n-3) n=2: a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +a(n-5) -a(n-6) n=3: [order 13] n=4: [order 27] n=5: [order 60] EXAMPLE Some solutions for n=5 k=4 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..0 ..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..0 ..0..1..0..0. .0..1..0..0. .1..0..0..0. .1..0..0..0. .0..1..0..0 ..0..1..1..0. .1..0..0..1. .0..1..1..0. .0..0..1..1. .1..0..0..0 ..0..0..0..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..0 CROSSREFS Column 2 is A078039. Row 1 is A000930(n+1). Row 2 is A264166. Sequence in context: A210211 A283054 A247358 * A180383 A133807 A325001 Adjacent sequences: A297221 A297222 A297223 * A297225 A297226 A297227 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 27 2017 STATUS approved

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Last modified December 4 16:41 EST 2022. Contains 358563 sequences. (Running on oeis4.)