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A302877
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 17, 10, 16, 13, 31, 35, 37, 21, 32, 21, 113, 72, 95, 82, 42, 64, 34, 363, 241, 306, 285, 209, 86, 128, 55, 813, 722, 1442, 1197, 858, 536, 179, 256, 89, 1751, 1821, 5871, 7580, 4849, 2938, 1549, 370, 512, 144, 5001, 4863, 21832, 41498
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OFFSET
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1,2
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COMMENTS
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Table starts
...1...2....3.....5......8.......13........21..........34...........55
...2...3...11....21.....31......113.......363.........813.........1751
...4...6...17....35.....72......241.......722........1821.........4863
...8..10...37....95....306.....1442......5871.......21832........89400
..16..21...82...285...1197.....7580.....41498......224087......1300510
..32..42..209...858...4849....45897....359518.....2795440.....24612087
..64..86..536..2938..23037...320405...3780984....44148194....588417750
.128.179.1549.11126.114810..2489823..44888558...786125894..15974455418
.256.370.4513.44216.603229.20679119.569313013.14827387374.460770487307
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 56] for n>59
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 60] for n>64
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1
..1..0..1..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..1..0..1
..1..0..1..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..1..0..1
..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..1
..1..1..0..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .1..1..0..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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