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A304931
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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5
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1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 53, 26, 26, 53, 13, 21, 105, 54, 73, 54, 105, 21, 34, 237, 101, 173, 173, 101, 237, 34, 55, 577, 186, 374, 452, 374, 186, 577, 55, 89, 1205, 361, 842, 1034, 1034, 842, 361, 1205, 89, 144, 2681, 700, 1923, 2265, 2653, 2265
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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......89.....144......233
..2....5...9...21....53...105....237....577...1205....2681....6349....13681
..3....9..13...26....54...101....186....361....700....1340....2562.....4913
..5...21..26...73...173...374....842...1923...4326....9786...22216....50282
..8...53..54..173...452..1034...2265...5306..12135...28127...66067...153211
.13..105.101..374..1034..2653...6426..16855..42256..110818..293243...759597
.21..237.186..842..2265..6426..15993..42032.107527..294610..802939..2150494
.34..577.361.1923..5306.16855..42032.118024.317161..963090.2839363..8199638
.55.1205.700.4326.12135.42256.107527.317161.920997.3074573.9708161.30250926
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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) +a(n-2)
k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)
k=3: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) +a(n-5) +a(n-6) -a(n-7) -a(n-11) -a(n-12)
k=4: [order 36] for n>37
k=5: [order 34] for n>45
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..1. .0..0..1..1. .0..1..1..1. .0..1..1..1
..0..0..0..0. .1..0..0..0. .0..1..1..1. .1..1..1..1. .1..1..1..1
..1..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..0. .1..1..1..1
..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .1..1..1..0
..0..0..0..1. .0..0..0..1. .1..0..1..1. .0..1..1..1. .0..1..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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