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A163734 Number of n X 3 binary arrays with all 1s connected, all corners 1, and no 1 having more than two 1s adjacent. 3
1, 2, 5, 9, 17, 39, 95, 217, 473, 1011, 2147, 4545, 9601, 20255, 42703, 90001, 189657, 399627, 842019, 1774105, 3737937, 7875575, 16593247, 34960681, 73659385, 155194435, 326982211, 688925201, 1451509889, 3058214319, 6443410959 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Same recurrence for A163696.
Same recurrence for A163715.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + a(n-4) - 2*a(n-5) + a(n-6) for n>=10.
Empirical g.f.: x*(1 - 2*x + 2*x^2 - 3*x^3 + x^4 + 6*x^5 + 4*x^6 - 3*x^7 - 2*x^8) / ((1 - x)^2*(1 - 2*x - x^4)). - Colin Barker, Feb 22 2018
EXAMPLE
All solutions for n=5:
...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
...1.0.1...1.0.1...0.0.1...0.0.1...1.0.1...1.0.1...0.0.1...1.0.1...1.0.0
...1.0.1...1.0.1...0.0.1...0.0.1...0.0.1...0.0.1...1.0.1...1.0.1...1.0.0
...1.0.1...1.0.1...0.0.1...1.0.1...0.0.1...1.0.1...1.0.1...0.0.1...1.0.0
...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...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
...1.0.0...1.0.1...1.0.1...1.0.0...1.0.0...1.0.1...0.0.1...1.0.1
...1.0.0...1.0.0...1.0.0...1.0.1...1.1.1...1.0.1...1.1.1...1.0.1
...1.0.1...1.0.0...1.0.1...1.0.1...0.0.1...1.0.0...1.0.0...1.0.1
...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.0.1
CROSSREFS
Sequence in context: A322304 A182992 A115851 * A336141 A184353 A019135
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 03 2009
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)