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A300881
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 52, 50, 16, 32, 138, 148, 148, 138, 32, 64, 383, 440, 589, 440, 383, 64, 128, 1063, 1367, 2264, 2264, 1367, 1063, 128, 256, 2951, 4297, 8739, 12369, 8739, 4297, 2951, 256, 512, 8193, 13510, 34693, 63507, 63507, 34693, 13510
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4......8.......16........32.........64.........128...........256
...2....7....18.....50......138.......383.......1063........2951..........8193
...4...18....52....148......440......1367.......4297.......13510.........42216
...8...50...148....589.....2264......8739......34693......138559........556973
..16..138...440...2264....12369.....63507.....345713.....1914083......10597966
..32..383..1367...8739....63507....447946....3260568....24521565.....184377268
..64.1063..4297..34693...345713...3260568...33392871...350899542....3640767606
.128.2951.13510.138559..1914083..24521565..350899542..5113575513...72955755546
.256.8193.42216.556973.10597966.184377268.3640767606.72955755546.1429279770363
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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) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)
k=3: [order 25] for n>26
k=4: [order 97] for n>98
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..0. .0..1..1..1
..0..1..1..1. .1..1..0..0. .1..0..1..0. .1..0..1..0. .0..1..1..0
..1..1..0..0. .1..1..1..0. .1..0..1..1. .1..0..1..0. .1..1..1..1
..0..1..1..0. .1..1..0..1. .1..1..1..0. .0..1..0..1. .0..1..0..0
..0..0..1..1. .1..0..1..0. .0..1..0..1. .1..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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