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 A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero. 12
 0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 5, 13, 0, 5, 18, 26, 15, 34, 0, 8, 50, 84, 74, 48, 89, 0, 13, 128, 309, 468, 200, 155, 233, 0, 21, 338, 1108, 2036, 2856, 530, 499, 610, 0, 34, 882, 3979, 10982, 14016, 17800, 1394, 1602, 1597, 0, 55, 2312, 14314, 53440, 122232 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table starts .0....1....1....2.......3........5..........8..........13............21 .0....2....2....8......18.......50........128.........338...........882 .0....5....5...26......84......309.......1108........3979.........14314 .0...13...15...74.....468.....2036......10982.......53440........271596 .0...34...48..200....2856....14016.....122232......813704.......6066698 .0...89..155..530...17800...100176....1366374....12824770.....133115004 .0..233..499.1394..110036...729297...15243860...204666568....2933712940 .0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404 .0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108 LINKS R. H. Hardin, Table of n, a(n) for n = 1..311 FORMULA Empirical for column k: k=1: a(n) = a(n-1) k=2: a(n) = 3*a(n-1) -a(n-2) k=3: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3) k=4: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3) k=5: [order 11] for n>12 k=6: [order 32] for n>33 k=7: [order 52] for n>54 Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) n=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) n=3: [order 20] EXAMPLE Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0 ..1..1..0..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0 ..1..0..1..0. .1..1..0..1. .1..1..1..1. .1..0..1..0. .1..1..0..0 ..0..1..0..1. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..1..1..1 ..0..0..1..1. .1..1..0..0. .0..1..0..0. .1..0..1..1. .0..0..1..1 CROSSREFS Column 2 is A001519. Row 1 is A000045(n-1). Row 2 is A175395(n-1). Sequence in context: A118658 A165912 A301823 * A171936 A071055 A183034 Adjacent sequences: A301996 A301997 A301998 * A302000 A302001 A302002 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 30 2018 STATUS approved

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Last modified March 31 04:34 EDT 2023. Contains 361627 sequences. (Running on oeis4.)