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A163733
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Number of nX2 binary arrays with all 1s connected, all corners 1, and no 1 having more than two 1s adjacent
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4
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1, 1, 2, 2, 4, 6, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Same recurrence for A163695
Same recurrence for A163714
Appears to coincide with diagonal sums of A072405. [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
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LINKS
| R. H. Hardin, Table of n, a(n) for n=1..100
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FORMULA
| Empirical: a(n)=a(n-1)+a(n-2) for n>=5
G.f.: (1-x^3)/(1-x-x^2) (conjecture). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
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EXAMPLE
| All solutions for n=8
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1
...0.1...1.0...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...0.1...0.1...0.1
...0.1...1.0...1.0...1.0...1.1...1.0...0.1...0.1...1.1...0.1...1.1...1.1...0.1
...0.1...1.0...1.0...1.1...0.1...1.0...0.1...0.1...1.0...1.1...1.0...1.0...1.1
...0.1...1.0...1.1...0.1...0.1...1.0...0.1...1.1...1.0...1.0...1.1...1.0...1.0
...0.1...1.0...0.1...0.1...0.1...1.1...1.1...1.0...1.0...1.0...0.1...1.1...1.1
...0.1...1.0...0.1...0.1...0.1...0.1...1.0...1.0...1.0...1.0...0.1...0.1...0.1
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1
------
...1.1...1.1...1.1
...1.0...1.0...1.0
...1.0...1.1...1.1
...1.1...0.1...0.1
...0.1...0.1...1.1
...1.1...1.1...1.0
...1.0...1.0...1.0
...1.1...1.1...1.1
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MATHEMATICA
| Join[{1, 1}, Table[2*Fibonacci[n], {n, 70}]] (* From Vladimir Joseph Stephan Orlovsky, Feb 10 2012 *)
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CROSSREFS
| Cf. A118658, A055389, A006355. [From R. J. Mathar (mathar(AT)srw.leidenuniv.nl), Aug 06 2009]
Cf.: A006355. [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
Sequence in context: A006355 A055389 * A198834 A084202 A053637 A000016
Adjacent sequences: A163730 A163731 A163732 * A163734 A163735 A163736
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KEYWORD
| nonn,changed
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net) Aug 03 2009
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