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Search: id:A163685
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| A163685 |
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Number of nX2 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent |
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+0
1
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| 1, 3, 5, 8, 13, 20, 32, 52, 85, 138, 223, 360, 582, 942, 1525, 2468, 3993, 6460, 10452, 16912, 27365, 44278, 71643, 115920, 187562, 303482, 491045, 794528, 1285573, 2080100, 3365672, 5445772, 8811445, 14257218, 23068663, 37325880, 60394542
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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R. H. Hardin, Table of n, a(n) for n=1..100
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FORMULA
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Empirical: a(n)=2*a(n-1)-a(n-2)+a(n-4) for n>=7
Empirical: G.f.: x*(-x^3-x^4+x^5-x-1)/((x^2-x+1)*(x^2+x-1)). a(n)=5*A000045(n)/2-A010892(n+1)/2, n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009]
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EXAMPLE
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All solutions for n=5
...1.0...1.0...1.1...1.1...1.0...1.1...1.0...1.1...1.0...1.0...1.1...1.1...1.1
...1.0...1.0...1.0...1.0...1.0...1.0...1.0...1.0...1.1...1.1...0.1...0.1...0.1
...1.1...1.1...1.1...1.1...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...1.1
...0.1...0.1...0.1...0.1...1.0...1.0...1.1...1.1...0.1...0.1...0.1...0.1...1.0
...0.1...1.1...0.1...1.1...1.1...1.1...0.1...0.1...0.1...1.1...0.1...1.1...1.1
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CROSSREFS
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Sequence in context: A035421 A035424 A099351 this_sequence A080614 A079122 A071679
Adjacent sequences: A163682 A163683 A163684 this_sequence A163686 A163687 A163688
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KEYWORD
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nonn
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AUTHOR
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Ron Hardin (rhhardin(AT)att.net) Aug 03 2009
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