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 A301951 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero. 12
 0, 1, 0, 1, 2, 0, 2, 5, 5, 0, 3, 16, 20, 13, 0, 5, 52, 123, 83, 34, 0, 8, 169, 680, 947, 342, 89, 0, 13, 549, 4070, 9084, 7326, 1411, 233, 0, 21, 1784, 23565, 98839, 120815, 56710, 5820, 610, 0, 34, 5797, 138014, 1029960, 2406169, 1608681, 439078, 24007, 1597, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table starts .0....1.....1........2..........3............5...............8 .0....2.....5.......16.........52..........169.............549 .0....5....20......123........680.........4070...........23565 .0...13....83......947.......9084........98839.........1029960 .0...34...342.....7326.....120815......2406169........45013365 .0...89..1411....56710....1608681.....58609226......1969215107 .0..233..5820...439078...21418808...1427656268.....86143630040 .0..610.24007..3399722..285190208..34776685046...3768464135104 .0.1597.99026.26323903.3797277789.847137052736.164856325277648 LINKS R. H. Hardin, Table of n, a(n) for n = 1..364 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) = 4*a(n-1) +a(n-2) -2*a(n-3) k=4: a(n) = 9*a(n-1) -8*a(n-2) -14*a(n-3) +4*a(n-4) +4*a(n-5) -a(n-6) k=5: [order 13] for n>15 k=6: [order 26] for n>28 k=7: [order 43] for n>47 Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6 n=3: [order 10] for n>12 n=4: [order 36] for n>40 EXAMPLE Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1 ..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..1..0..1 ..0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..1..0. .0..0..1..0 ..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0 ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1 CROSSREFS Column 2 is A001519. Row 1 is A000045(n-1). Row 2 is A232317(n-1). Sequence in context: A133394 A305628 A094721 * A144529 A319498 A349782 Adjacent sequences: A301948 A301949 A301950 * A301952 A301953 A301954 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 29 2018 STATUS approved

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Last modified December 6 18:14 EST 2023. Contains 367614 sequences. (Running on oeis4.)