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 A301823 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero. 11
 0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 4, 13, 0, 5, 18, 25, 8, 34, 0, 8, 50, 74, 68, 16, 89, 0, 13, 128, 278, 299, 177, 32, 233, 0, 21, 338, 968, 1351, 1197, 457, 64, 610, 0, 34, 882, 3450, 6653, 6501, 4785, 1183, 128, 1597, 0, 55, 2312, 12210, 30441, 47363, 31061, 19130, 3075 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table starts .0....1...1....2......3.......5.........8.........13..........21............34 .0....2...2....8.....18......50.......128........338.........882..........2312 .0....5...4...25.....74.....278.......968.......3450.......12210.........43316 .0...13...8...68....299....1351......6653......30441......146175........682879 .0...34..16..177...1197....6501.....47363.....284691.....1896274......11958940 .0...89..32..457...4785...31061....333335....2626219....23877827.....205351902 .0..233..64.1183..19130..147954...2341241...24102055...298497818....3505205058 .0..610.128.3075..76499..705180..16471479..221373169..3746076847...60097022948 .0.1597.256.8018.305959.3364845.115975709.2034255683.47059520355.1030456894273 LINKS R. H. Hardin, Table of n, a(n) for n = 1..416 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) = 2*a(n-1) k=4: a(n) = 6*a(n-1) -13*a(n-2) +13*a(n-3) -6*a(n-4) +a(n-5) k=5: a(n) = 8*a(n-1) -22*a(n-2) +28*a(n-3) -17*a(n-4) +4*a(n-5) for n>7 k=6: [order 16] for n>17 k=7: [order 26] for n>28 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 14] for n>18 n=4: [order 66] for n>72 EXAMPLE Some solutions for n=5 k=4 ..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .0..0..0..0 ..1..1..1..1. .1..1..0..0. .0..1..0..1. .0..1..0..0. .1..1..0..1 ..0..0..1..0. .1..1..1..1. .1..0..1..1. .1..1..0..0. .1..0..1..0 ..0..1..0..1. .0..0..1..1. .0..0..0..0. .1..1..0..0. .0..1..0..1 ..0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1 CROSSREFS Column 2 is A001519. Column 3 is A000079(n-1). Row 1 is A000045(n-1). Row 2 is A175395(n-1). Sequence in context: A300822 A118658 A165912 * A301999 A171936 A071055 Adjacent sequences: A301820 A301821 A301822 * A301824 A301825 A301826 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 27 2018 STATUS approved

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Last modified December 7 05:34 EST 2023. Contains 367630 sequences. (Running on oeis4.)