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A302224
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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13
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0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 43, 34, 0, 5, 146, 164, 194, 111, 0, 8, 537, 760, 934, 675, 361, 0, 13, 1934, 3425, 6110, 4237, 2666, 1172, 0, 21, 6861, 15569, 38736, 40395, 21777, 9819, 3809, 0, 34, 24386, 70323, 251254, 338204, 292781, 105585, 37382
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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
.0.....3.....14......45.......146........537........1934..........6861
.0....11.....43.....164.......760.......3425.......15569.........70323
.0....34....194.....934......6110......38736......251254.......1610569
.0...111....675....4237.....40395.....338204.....3018243......26373655
.0...361...2666...21777....292781....3420704....42508145.....524715109
.0..1172...9819..105585...2043848...32181643...553097760....9458629708
.0..3809..37382..523414..14419536..310963650..7403262824..177191137344
.0.12377.140039.2578424.101511446.2973099477.97939043966.3265007473096
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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) -2*a(n-4)
k=3: [order 11]
k=4: [order 30] for n>34
k=5: [order 92] for n>97
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 15] for n>17
n=4: [order 54] for n>58
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..1..1..1. .1..1..0..1. .0..1..0..1. .1..1..1..0. .0..1..1..1
..1..0..0..0. .1..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..0
..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..1..1..1. .0..0..1..1
..0..0..0..0. .1..1..1..0. .0..0..0..0. .0..0..1..1. .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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