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A301823
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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.
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11
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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
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OFFSET
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1,5
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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