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A163714
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Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent.
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3
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3, 7, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338
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OFFSET
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1,1
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COMMENTS
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Same recurrence for A163695.
Same recurrence for A163733.
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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) = a(n-1) + a(n-2) for n>=5.
Conjectures from Colin Barker, Feb 22 2018: (Start)
G.f.: x*(1 + x)*(3 + x - x^2) / (1 - x - x^2).
a(n) = (2^(-n)*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / sqrt(5) for n>2.
(End)
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EXAMPLE
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All solutions for n=4:
...1.0...1.0...1.1...1.1...0.1...0.1...1.1...1.1...1.0...1.1...1.0...1.0...0.1
...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...1.0...1.0...1.1...1.1...0.1
...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...1.1...1.1...0.1...0.1...1.1
...1.0...1.1...1.0...1.1...0.1...1.1...0.1...1.1...0.1...0.1...0.1...1.1...1.0
------
...1.1...0.1...0.1
...0.1...1.1...1.1
...1.1...1.0...1.0
...1.0...1.0...1.1
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CROSSREFS
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Cf. A090991, A078642, A047992. - R. J. Mathar, Aug 06 2009
Sequence in context: A088636 A114113 A100056 * A333910 A307191 A234638
Adjacent sequences: A163711 A163712 A163713 * A163715 A163716 A163717
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Aug 03 2009
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STATUS
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approved
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